Rational Exponet Equations:

Question

Help?

1.(x^2+9x+22)^3/2 = 8

2.(5x-5)^2/3 = 16

Answer 1

1.
raise both sides to the 2/3 , notice that 2/3 is the reciprocal of 3/2

[ (x^2 + 9x + 22)^(3/2) ] ^(2/3) = 8^(2/3)
(x^2 + 9x + 22)^1 = 8^(2/3)

x^2+9x+22 = 4
x^2 + 9x + 18 = 0
(x+6)(x+3) = 0
x = -6 or x = -3

Since we effectively squared both sides, ( ^(2/3) is the same as taking the cube root, then squaring), all answers must be verified.

if x = -6
LS = (36 - 54 + 22)^(3/2
= 4^(3/2) = 8
= RS

if x=-3
LS = (9-27+22)^(3/2)
= 4^(3/2) = 8
= RS

so x=-6 or x=-3

You try the second one in the same way.