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Julli [10]
3 years ago
12

what is the solution of sqrt(2x+4)-sqrt(x)=2 A. x = 0 B. x = 0 and x = 16 C. x = 0 and x = –16 D. x = 16 and x = –16

Mathematics
2 answers:
Charra [1.4K]3 years ago
5 0
We want to solve
√(2x+4) - √(x) = 2

Write equation as
√(2x+4) = √x + 2
Square each side.
2x + 4 = x + 4√x + 4
x = 4√x
x - 4√x = 0
√x (√x - 4) = 0

Either 
√x = 0 => x = 0
or
√x = 4 => x = 16

Test for extraneous solutions.
When x = 0:
√(2x+4) - √x = 2  (Correct)
When x = 16:
√(2x+4) - √x = √(36) - √(16) = 6 - 4 = 2 (Correct)

A plot of f(x) = √(2x+4) - √x - 2 = 0 confirms hat the solutions are correct.

Answer: B. x = 0 and x = 16.

levacccp [35]3 years ago
3 0
The answer is a, x is 0
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