What is the answer to 4+sqrt(x^2-x-2)=x^2-x ?

The answer to 4+sqrt(x^2-x-2)=x^2-x is x=-2,x=3

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

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

x = - 2, x = 3

Solution steps

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

Remove square roots

x^{2} - x - 2 = x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 16

Solve

x^{2} - x - 2 = x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 16 : x = - 2, x = 3, x = \frac{1 + 13}{2}, x = \frac{1 - 13}{2}

x = - 2, x = 3, x = \frac{1 + 13}{2}, x = \frac{1 - 13}{2}

Verify Solutions:

x = - 2

True

, x = 3

True

, x = \frac{1 + 13}{2}

False

, x = \frac{1 - 13}{2}

False

The solutions are

x = - 2, x = 3

6 - x = - x

x^{2} + x - 2 = x^{2} + x - 4

4 x + 40 = x + 7

73 - n - 116308 n = 0

2 x + 8 - 6 = - 4

What is the answer to 4+sqrt(x^2-x-2)=x^2-x ?
The answer to 4+sqrt(x^2-x-2)=x^2-x is x=-2,x=3
Solve for x: 4+sqrt(x^2-x-2)=x^2-x
The solution is x=-2,x=3