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hala718 eNotes educator| Certified Educator

(x^2 -9)^1/2 = 4

First we will square both sides:

==> ((x^2 -9)^1/2)^2 = 4^2

==> (x^2 -9) = 16

Now add 9 to both sides:

==> x^2 = 25

==> x= +-5

 

giorgiana1976 | Student

To eliminate the square root, we'll raise to square both sides of the equation:

[( x^2 - 9)^(1/2)]^2 = 4^2

We'll eliminate the square root from the left side :

x^2 - 9 = 16

We'll add 9 both sides:

x^2 = 25

x1 = +sqrt25

x1 = 5

x2 = -5

We'll verify the solutions into equation:

sqrt(25-9) = 4

sqrt16 = 4

4 = 4

sqrt((-5)^2-9) = 4

sqrt(25-9) = 4

4 = 4

The equation will have 2 solutions, x=5 and x2=-5.
neela | Student

To solve for (x^2-9)^(1/2) = 4.

Square both sides.

x^2-9 = 4^2 = 16

x^2 = 16+9 .

x^2 =25

x^2-5^2  = 0.

(x-5)(x+5) = 0.

x-5 =0, x+5 = 0

x=5 ,or x= -5.

 

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