What is the answer to sqrt(2+x)-sqrt(2-x)=x ?

The answer to sqrt(2+x)-sqrt(2-x)=x is x=0,x=2,x=-2

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sqrt(2+x)-sqrt(2-x)=x

2 + x - 2 - x = x

x = 0, x = 2, x = - 2

Solution steps

2 + x - 2 - x = x

2 + x = x^{2} + 2 2 - x x + 2 - x

Subtract

x^{2} + 2 2 - x x + 2 - x

from both sides

2 + x - (x^{2} + 2 2 - x x + 2 - x) = x^{2} + 2 2 - x x + 2 - x - (x^{2} + 2 2 - x x + 2 - x)

Simplify

- x^{2} + 2 x - 2 2 - x x = 0

Factor

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

- x (x - 2 + 2 2 - x) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 2 + 2 2 - x = 0

Solve

x - 2 + 2 2 - x = 0 : x = 2, x = - 2

x = 0, x = 2, x = - 2

Verify Solutions:

x = 0

True

, x = 2

True

, x = - 2

True

The solutions are

x = 0, x = 2, x = - 2

x + 4 - 7 = 1

- x - 3 + 5 = 3

2 x + 4 = 4

100 = 25 t

What is the answer to sqrt(2+x)-sqrt(2-x)=x ?
The answer to sqrt(2+x)-sqrt(2-x)=x is x=0,x=2,x=-2
Solve for x: sqrt(2+x)-sqrt(2-x)=x
The solution is x=0,x=2,x=-2