Question

If (a+b)^2 = 25, and "a" and "b" are negative integers, what is the value of (a+b)^3?

Answer 1

Squaring makes the first one positive. So if you are multiplying 3 negatives, you get....?

And since the answer to the first is 25, you know what a and b add up to, right?

Answer 2

multiplying 3 negatives = positive because - times - = + and + times - = - and - times - = +

so then (-5+-5)^3 = -1000

wait that's not right...

the answer is supposed to be -125

Answer 3

Ohhhhhh it's 2 and 3 not 5

Answer 4

multiplying 3 negatives gets you a negative.

I didn't say a and b were each -5. I said you know what they add up to be squared to 25.

It doesn't matter what a and b are individually in this problem.

So, since you know that a and b add to -5, then -5^3 is your answer.

Answer 5

ok, i get it. was just misunderstanding what was being asked. is there another way of solving this?

Answer 6

multiplying 3 negatives = positive because - times - = + and + times - = - and - times - = +

And what you did here was multiply 4 negatives. :)

Answer 7

Take the square root of both sides. (a+b)= +or - 5 (in this case we know it's -5 because they tell you a and b are both negatives. Then put it into the (a+b)^3=? equation.

Answer 8

i don't understand what u mean by the first part. do u mean the square root of -5 or the 25? or

Answer 9

The square root of (a+b) squared is just (a+b), right? And when you take the square root of something, the answer can either be positive or negative, so the square root of 25 is either +5 or -5.

Answer 10

oh ohhhh, but how do u know which one to use, +5 or -5?

Answer 11

Well, in this case, they told you that a and b are both negative numbers, so you know it HAS to be the -5. But in other cases, they could both be right. You read the details carefully. But to check, you just plug your answers back into the original equation and see if the equation is true. :)

Answer 12

I suspect what they were really trying to get you to see from this problem is that if you cube a negative, you get a negative.

Answer 13

i feel silly, ure right, i need to b more meticulous.

Answer 14

It's ok. I tend to forget minor details when it's my own work. :) There's no pressure on me when I'm helping someone else, so I'm more detail-oriented.

Answer 15

hahaha it happens. can i tell u the steps of solving this equation both ways after u explained it? just to make sure i got it 110%

Answer 16

OK.

(a+b)^2=25
(a+b) = -5 (take the square root of both sides)

Since we know that (a+b)=-5, we can put it in the second equation.

(-5)^3=??
=-125

Answer 17

i meant could i explain it the way u told me, but that's great too. thank you

Answer 18

was that the second way of solving this equation?

Answer 19

That is how I explained it except I used words instead of numbers.

Answer 20

i meant that i wanted to tell u how to solve it and have u check my work lol okok thank you!
wait, i still don't know, is there a 2nd way of solving this? or just that one way that u showed me?

Answer 21

I suppose you could use the guess-and-check method of solving it (where you just keep guessing random numbers until you get the answer), but that would take forever.

And I solved it for you up there. :) The answer is -125.

Answer 22

hahaha i guess that is a possible option, check and guess. we were just preparing for the psat and this was one of the qs i got wrong and the teacher told us we needed to solve it 2 ways.

Answer 23

I can't think of an easy second way. Maybe someone else will come along and give you one. :) Sorry!

Answer 24

oh it's completely alright, u've been a great help. I literally would not have gotten anywhere without ur help. thank you

Answer 25

My pleasure. :)

Answer 26

if i hv more q's can u please help again, if u can?

Answer 27

Sure. :)

Answer 28

ure the best! (:

Answer 29

hey Becki?

Answer 30

Yes?

Answer 31

\[\sqrt{x}-4 > 1\]
how many positive integers (x) satisfy the inequality?

Answer 32

i dont't understand wat steps i need to take to solve this

Answer 33

wud i hv to isolate the variable first?

Answer 34

Yes. :)

Answer 35

wait i wrote it wrong, its' radical 4-x then out of radical its greater than 1

Answer 36

oh ok

Answer 37

so then i wud hv radical 3 is greater tan x?

Answer 38

So is it\[\sqrt{4-x}>1\]

Answer 39

yes that is correct

Answer 40

So square both sides to get rid of the radical.

Answer 41

wud i bring over the x on the right side or keep it under radical?

Answer 42

ohhhhh ok squaring, so then i wud hv x^2 - 8X +16 is greater than 1

Answer 43

then subtract 16 from the other side so it wud be -15?

Answer 44

No. When you square something that's under a radical, you just have what's under the radical. Think like this:

\[\sqrt{2}\times \sqrt{2}=2\]

Answer 45

so then it wud be \[\sqrt{4-x} \times \sqrt{4-x}\]

Answer 46

yes....which is?

Answer 47

my calculator says "ERROR" lol

Answer 48

Yeah, you can't do it on a calculator. Remember, when you square the square root of something, you are left with the something.

Answer 49

so it will just b 4-x?

Answer 50

OHHH

Answer 51

Yes. :)

so 4-1>1

Answer 52

i get it, like from ur example

Answer 53

omgosh ure a genius

Answer 54

okok one sec let me solve

Answer 55

sooooo, \[x <3\]

Answer 56

and that means that there are only #'s left, which are 1 and 2 and so the answer is two positive integers

Answer 57

You got it. :)

Answer 58

ahh ure amazing, it's so easy with ur help!

Answer 59

is this the only method of solving this equation?

Answer 60

Guess and check is the only other way I can think of . :)

Answer 61

probably the only other method for most of them.

Answer 62

THANK YOU SO MUCH again lol :)

Answer 63

You're welcome. :)

Answer 64

can u help with another? lol sorry!

Answer 65

sure.

Answer 66

In the sequence above, the first term is \[- \frac{ 3 }{ 16 }\] and each term after the first is -4 time the preceding term. wat is the result of dividing the 50th term by the 48th term?

Answer 67

oh here's the sequence

Answer 68

\[- \frac{ 3 }{ 16 }, \frac{ 3 }{ 4 }, -3, 12, -48,...\]

Answer 69

Ooh. Now you're making me think! :) I like it.

Answer 70

hahaha im sorry

Answer 71

i just have absolutely no clue as to where to start with this equation

Answer 72

No, it's fine. Give me a sec. I love puzzles. :)

Answer 73

hehehe alright, take ur time! (:

Answer 74

I know the answer off the top of my head, now I just need to figure out how to explain to you how to do it.

Answer 75

that was so quick! lol ik the answer is 16

Answer 76

Yup. And it's because you're multiplying by -4 each time, so -4x-4=16. The ratio between 50 and 48, because you're multiplying each by -4, is 16. Let's see....OH!

I think i have it....just a sec.

Answer 77

\[\frac{ n(4x4) }{ n }\]

So, if you have a number n (that would be your 48th number in this case), and you're dividing it into that number nx-4x-4, wouldn't you get 16? It wouldn't really matter what numbers in the sequence you use as long as the numbers are 2 apart in the sequence. Does that make sense?

Answer 78

it makes sense but let me just read it a few times to process lol one sec

Answer 79

ok so i understand how they got the sequence (by x by -4), but i dont understand how we know what the 48the and 50th terms are..or is the 48th term the -48 in the sequence? so then do u multiply to get 192 and then multiply 192 by -4 = -768....wait no, no scratch that

Answer 80

We don't need to know the 48th or 50th terms. It wouldn't matter. All that matters is we know that the top number is the bottom number times (-4) twice.

Answer 81

Try it with any 2 other terms that are 2 places apart in the sequence. Try it with -3 and -48...

Answer 82

And the question doesn't ask you to identify the 48th and 50th terms. It just asks you for the ratio.

Answer 83

OHHHHH i see. when i divide -48 by -3 i get 16

Answer 84

ohhh alright, cool

Answer 85

other method of solving wud b guess and check again, right? haha

Answer 86

Right?? I love numbers. They always do what they're supposed to do. :)

Yeah, no other methods, once again. :) I have no idea what your teacher could be talking about.

Answer 87

me either........lol

Answer 88

thank you thank you thank you

Answer 89

Again, you're welcome. I'm a total nerd. I got on here once for help in calculus and now I'm addicted to helping other people. I love this stuff.

Answer 90

Come find me again sometime if you ever need help again. You're fun because you don't want me to feed you the answers like some that are here. :)

Answer 91

heheheh yes, I'd really like to learn how to do them, i just need some guidance and u were really super helpful. thank so much! and i can c how it can become addicting, it's fun!