math problem 10pts. ASAP?

niem-n

solve this please

(16 - x)^.5 + (x +13)^.5 = 7

I think it has to do something with a^2 + 2ab + b^2, lol

daniel-piper

Quick solution: x=12 or x=-9

For worked solution observe below:

sqrt(16-x) + sqrt(x+13) = 7 square each side

(16-x) + (x+13) + 2*sqrt(16-x)*sqrt(x+13) = 49 simplify

29 + 2*sqrt((16-x)*(x+13)) = 49 simplify

sqrt((16-x)*(x+13)) = (49-29)/2 = 10 square each side again

(16-x)*(x+13) = 100 expand

-x^2 + 16x - 13x + 208 = 100 move everything to the left

-x^2 + 3x + 108 = 0 multiply everything by -1 then factor

(x-12)(x+9) = 0 and solve

x=12 or x=-9

Hope this helps!

michael

sqr = square root

x^1/2 = sqr(x)

[sqr(16 - x) + sqr(x + 13)] ^2 = 49 // Square both sides to simplify

[sqr(16 - x) + sqr(x + 13)] ^2 = 49

==> [sqr(16 - x) + sqr(x + 13)][sqr(16 - x) + sqr(x + 13)] = 49

==> (16 - x) + 2 sqr(16 - x)sqr(x + 13) + (x + 13) =

==> 2 sqr[(16 - x)(x + 13)] + 29 = 49 // evaluate

2 sqr[(16 - x)(x + 13)] = 20 // subtract 29 on both sides to isolate x on the left side

sqr[(16 - x)(x + 13)] = 10 // divide both sides by 2 to simplify

(16 - x)(x + 13) = 100 // Square both sides to eliminate the sqr

(16 - x)(x + 13) - 100 = 0

==> -x^2 + 3x + 108 = 0 // write quadratic polynomial

-((x - 12)(x + 9) = 0 // factor

(x - 12)(x + 9) = 0 // multiply by -1 to simplify

x = 12 or -9 is your answer.

riley-ross_609d77e9b3143

You're right, because the first step is to square both sides,

using the perfect square rule you cited.