Question

Solve: 2sqrt{x+5}+3sqrt{x-3}=9

Answer 1

I keep coming up with 88/13

Answer 2

4

Answer 3

4 is the correct answer. to solve it
1.) first square on both sides and simplify. You will get
\[12\sqrt{(x+5)(x-3)} = 88-13x\]
2.) then again square it on both the sides and simplify. You will end up with a quadratic equation.
3.) If you solve that quadratic equation you will get x=4 as one of the solutions.
4.) You can verify it by substituting it back into the equation given.

Answer 4

if i square both sides in the first step doesn't that make the equation
\[4(x+5)+9(x-3)=81\]

Answer 5

no

Answer 6

\[(a+b)^2=a^2+2ab+b^2\]

Answer 7

o right thanks.

Answer 8

\[2\sqrt{x+5}+3\sqrt{x-3}=9\] that is the equation you were using the first time right?

Answer 9

\[(2\sqrt{x+5}+3\sqrt{x-3})^{2}=9^{2}\]
\[(2\sqrt{x+5})^{2}+2*(2\sqrt{x+5})*(3\sqrt{x-3})+(3\sqrt{x-3})^{2}=9^{2}\]

Answer 10

\[4(x+5)+12*(\sqrt{x+5})*(\sqrt{x-3})+9(x-3) = 81\]

Answer 11

if i square this equation i get 144(x+5)(x-3)=7744-2288-169x^2

Answer 12

For (2sqrt(x+5) + 3sqrt(x-3))^2 I come up with 13x-7+12sqrt(x+5)(x-3)

Answer 13

i got something ugly so far
25x^2-2576x+9904=0

Answer 14

on simplifying you get 88-13x=12√(x+5)(x-3) right?

Answer 15

then square it..

Answer 16

but it looks ugly then

Answer 17

apparently the answer is 4. I typed into wolframs and that what it gave me

Answer 18

@myininaya you squared that???

Answer 19

if you square 88-13x. I get 7744-2288=169x^(2)

Answer 20

144(x+5)(x-3)=7744-2288-169x^2 do we get this... man this is very ugly

Answer 21

i have to check my answers now since i raised both sides to even power

Answer 22

but like 99.04 is totally not going to work

Answer 23

so the answer is just 4

Answer 24

can you read my attachment raioner?

Answer 25

yes im looking it over now

Answer 26

trying to find out where i went wrong thanks for doing that for me.

Answer 27

np
those were some ugly numbers

Answer 28

ya right.. but why is 99.04 wrong? because of the domain of x right?

Answer 29

whell if you plug it in both sides are not the same

Answer 30

this is part of my take home test and and the entire test is like this.

Answer 31

root of something is geater than 0.. so x-3 greater than 0 and x=5 greater than 0...

Answer 32

*x+5

Answer 33

Ok, when you square both sides of the equation, you will come up with (x-4)(25x-2476)=0 so you'll want to set both sides of the equation to equal 0 x-4=0, 25x-2476=0 so you'll have x=4 and x=2476/25 now plug into the original equation start with 4 (because it looks easy :) ) and you'll find 4 works, you can test 2476/25 as well but no need, myininaya already confirmed x=4 :D

Answer 34

ya but you can also take the domain stuff in consideration no need to verify then..

Answer 35

whenever you raise both sides to an even power you should always check your answers

Answer 36

ya squaring increasing the number roots..

Answer 37

Very true

Answer 38

he will get irritated finding the answer and verifying 99.04 will surely eat his head up.. lol!

Answer 39

i would make my calculator do the arithmetic which i did lol

Answer 40

gn guys