Question

Find two consecutive even integers such that the square of the smaller is 10 more than the larger.

Answer 1

I'm a bit confused in solving this

Answer 2

let the nos be x and x+2
x^2-(x+2)=10

Answer 3

you might have thought it was : x^2-(x+2)^2. isnt it?

Answer 4

ya

Answer 5

=10

Answer 6

ya, that's a grammatical problem in the question.

Answer 7

hey where r u from?

Answer 8

I'm from NY my teacher just can't write out word problem

Answer 9

I still don't get how you it...

Answer 10

Something is wrong with my work. Anybody know?

Let x and x+2 be consecutive even integers given that x is even.

x^2 = 10(x+2)
x^2 = 10x + 20
x^2 – 10 x – 20 = 0

Answer 11

Two even consecutive integers, they are like 2,4 or 4,6 or 8,10 or just x, x+2(where x is an even number). Is this clear?
The smaller number is x and larger is x+2.
The problem says that the square of the smaller number(x^2) is 10 more than the larger number(x+2).
x^2=10+(x+2)
or x^2-(x+2)=10
Please tell me if you didnt understand.
@directrix, The square of the smaller no is 1O more than the larger number, not 10 times the larger number.

Answer 12

I understand the first statement

Answer 13

Ten MORE than, not ten TIMES.
@Mani --> I read incorrectly. Thanks for telling me. Now, I will re-work the problem.

Answer 14

So, 4 and 6 would be one pair.

Then, I got -3 but it is odd and is still odd when I add 2 and get -1. Therefore, x = -3 is an extraneous root for this scenario. Yes?

Answer 15

The answer is 4,6. See that the square of 4 is 16, which is 10 more than 6.
In algebra, you have got to treat values like x and x+2 just as normal numbers. So, if x is a no, its square is x^2. And if it is 10 more than the lager no.
x^2=10+(x+2){compare this with 16=10+6}
@directrix, x=-3 is a solution for the equation but not of this problem, because the problem asks for even integers. Is that the meaning of 'extraneous'?

Answer 16

Never knew things could be become complicated than it seems

Answer 17

I thought so but then I read this.

Extraneous Solution
Spurious Solution

A solution of a simplified version of an equation that does not satisfy the original equation. Watch out for extraneous solutions when solving equations with a variable in the denominator of a rational expression, with a variable in the argument of a logarithm, or a variable as the radicand in an nth root when n is an even number.

http://www.mathwords.com/e/extraneous_solution.htm

Answer 18

@pokemon23 , i am sorry that i am unable to explain this to you. But can you tell me what is it about the problem that you dont get?

Answer 19

I mean, the exact part where u dont understand

Answer 20

While the Poke is thinking, I'll post a problem about sequences. Maybe you will work on it. Just a sec.

Answer 21

umm Let after you got x^2=10x(x+2) how did you get x= to 4 and 6

Answer 22

Oh, sorry I skipped a few steps.
x^2=10+(x+2)
x^2-x-2=10
x^2-x-12=0
x^2-4x+3x-12=0
x(x-4)+3(x-4)=0
(x+3)(x-4)=0
So, you get either x=-3 or x=4.
But the question asks for even integers, so we get only x=4.
And so the even integer consecutive to it is x+2=6.
Now, is it ok?

Answer 23

ya ok because I was wondering like how did he do this thanks for the help and direct as well

Answer 24

@ Mani, I get it, too.. Thanks.
Will you work on the problem I just posted?