If (x + 3)^2 = 25 and x > 0, what is the value of x^2 - 1? — GMAT

If $(x + 3)^2 = 25$ and $x > 0$ , what is the value of $x^2 - 1$ ?

Taking the square root of both sides of

(x + 3)^2 = 25

gives

x + 3 = \pm 5

. Since

x > 0

, we choose

x + 3 = 5

, which gives

x = 2

. Substituting

x = 2

into

x^2 - 1

produces

2^2 - 1 = 3

Take the square root of both sides of the given quadratic equation

x + 3 = 5

x + 3 = -5

The equation

(x + 3)^2 = 25

implies

x + 3

can be either positive or negative 5.

Solve for

x

under the constraint

x > 0

x = 2

From

x + 3 = 5

, we obtain

x = 2

. The second root

x = -8

is discarded because

x > 0

Substitute

x = 2

into the target expression

x^2 - 1

2^2 - 1 = 3

Evaluating

x^2 - 1

x = 2

yields

4 - 1 = 3

Solving Quadratic Equations by Taking Square Roots

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