Posted by **Sam'** on Wednesday, August 22, 2012 at 6:54am.

Rational Exponet Equations:

Help?

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

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

- Algebra2 -
**Reiny**, Wednesday, August 22, 2012 at 8:04am
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.

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