What is the answer to sqrt(x-3)+sqrt(x+5)=(16)/x ?

The answer to sqrt(x-3)+sqrt(x+5)=(16)/x is x=4

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sqrt(x-3)+sqrt(x+5)=(16)/x

x - 3 + x + 5 = \frac{16}{x}

x = 4

Solution steps

x - 3 + x + 5 = \frac{16}{x}

Multiply both sides by

x

x - 3 x + x + 5 x = \frac{16}{x} x

Simplify

x - 3 x + x + 5 x = 16

Remove square roots

64 x^{4} + 4096 x^{2} + 65536 = 1024 x^{3} + 5120 x^{2}

Solve

64 x^{4} + 4096 x^{2} + 65536 = 1024 x^{3} + 5120 x^{2} : x = 4, x \approx 16.73754 \dots

x = 4, x \approx 16.73754 \dots

Verify Solutions:

x = 4

True

, x \approx 16.73754 \dots

False

The solution is

x = 4

5 x + 44 + 3 = 11

x^{\frac{2}{3}} - 2 x^{\frac{1}{3}} - 3 = 0

6 x - \frac{3}{1 - x ^{2}} = 0

3 x + 4 - x - 4 = 2 x

x + 2 = 2 x - 3

What is the answer to sqrt(x-3)+sqrt(x+5)=(16)/x ?
The answer to sqrt(x-3)+sqrt(x+5)=(16)/x is x=4
Solve for x: sqrt(x-3)+sqrt(x+5)=(16)/x
The solution is x=4