What is the answer to 3+sqrt(-x^2+4)=x^2-1 ?

The answer to 3+sqrt(-x^2+4)=x^2-1 is x=2,x=-2

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3+sqrt(-x^2+4)=x^2-1

3 + - x^{2} + 4 = x^{2} - 1

x = 2, x = - 2

Solution steps

3 + - x^{2} + 4 = x^{2} - 1

Remove square roots

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

Solve

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

x = 2, x = - 2, x = 3, x = - 3

Verify Solutions:

x = 2

True

, x = - 2

True

, x = 3

False

, x = - 3

False

The solutions are

x = 2, x = - 2

4 x = 2 x - 3

5 x - 2 = x + 9

3 = 12 x - 36 \cdot x^{2} + 9

What is the answer to 3+sqrt(-x^2+4)=x^2-1 ?
The answer to 3+sqrt(-x^2+4)=x^2-1 is x=2,x=-2
Solve for x: 3+sqrt(-x^2+4)=x^2-1
The solution is x=2,x=-2