What is the answer to sqrt(1+x*\sqrt{2x^2+8)}=x+1 ?

The answer to sqrt(1+x*\sqrt{2x^2+8)}=x+1 is x=0,x=2

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sqrt(1+x*\sqrt{2x^2+8)}=x+1

1 + x \cdot 2 x^{2} + 8 = x + 1

x = 0, x = 2

Solution steps

1 + x 2 x^{2} + 8 = x + 1

Square both sides:

1 + x 2 x^{2} + 8 = x^{2} + 2 x + 1

1 + x 2 x^{2} + 8 = x^{2} + 2 x + 1

Subtract

x^{2} + 2 x + 1

from both sides

1 + x 2 x^{2} + 8 - (x^{2} + 2 x + 1) = x^{2} + 2 x + 1 - (x^{2} + 2 x + 1)

Simplify

- x^{2} + 2 x^{2} + 8 x - 2 x = 0

Factor

- x^{2} + 2 x^{2} + 8 x - 2 x : - x (x - 2 x^{2} + 8 + 2)

- x (x - 2 x^{2} + 8 + 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 2 x^{2} + 8 + 2 = 0

Solve

x - 2 x^{2} + 8 + 2 = 0 : x = 2

x = 0, x = 2

Verify Solutions:

x = 0

True

, x = 2

True

The solutions are

x = 0, x = 2

x - 6 + 8 = x

3 x^{2} + 10 x - 83 = 0

x, 2 x + y = 5

\frac{x}{x} + 1 + x + \frac{1}{x} = \frac{17}{4}

x^{2} + 9 - x = 3

What is the answer to sqrt(1+x*\sqrt{2x^2+8)}=x+1 ?
The answer to sqrt(1+x*\sqrt{2x^2+8)}=x+1 is x=0,x=2
Solve for x: sqrt(1+x*\sqrt{2x^2+8)}=x+1
The solution is x=0,x=2