What is the answer to sqrt(x+7)+sqrt(x+2)=(15)/((sqrt(x+7))) ?

The answer to sqrt(x+7)+sqrt(x+2)=(15)/((sqrt(x+7))) is x=2

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sqrt(x+7)+sqrt(x+2)=(15)/((sqrt(x+7)))

x + 7 + x + 2 = \frac{15}{( x + 7 )}

x = 2

Solution steps

x + 7 + x + 2 = \frac{15}{( x + 7 )}

Multiply both sides by

x + 7

x + 7 x + 7 + x + 2 x + 7 = \frac{15}{x + 7} x + 7

Simplify

(x + 7)^{2} + x + 7 x + 2 = 15

Expand

(x + 7)^{2} + x + 7 x + 2 : x + 7 + x + 7 x + 2

x + 7 + x + 7 x + 2 = 15

Remove square roots

x^{2} + 9 x + 14 = x^{2} - 16 x + 64

Solve

x^{2} + 9 x + 14 = x^{2} - 16 x + 64 : x = 2

x = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

3 x^{2} + 7 5 x + 2 = 0

\frac{1}{3 \cdot x - 1 + 2} = 5

a, a \cdot b^{2} = b \cdot a

(\frac{20 + x}{x}) + (\frac{20 - x}{x}) = 6

x - 2 = x - 8

What is the answer to sqrt(x+7)+sqrt(x+2)=(15)/((sqrt(x+7))) ?
The answer to sqrt(x+7)+sqrt(x+2)=(15)/((sqrt(x+7))) is x=2
Solve for x: sqrt(x+7)+sqrt(x+2)=(15)/((sqrt(x+7)))
The solution is x=2