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

The answer to sqrt(x^2-1)+3=x^2 is x=sqrt(5),x=-sqrt(5)

Solve for x: sqrt(x^2-1)+3=x^2

The solution is x=sqrt(5),x=-sqrt(5)

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

x = 5, x = - 5

Decimal Notation

x = 2.23606 \dots, x = - 2.23606 \dots

Solution steps

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

Remove square roots

x^{2} - 1 = x^{4} - 6 x^{2} + 9

Solve

x^{2} - 1 = x^{4} - 6 x^{2} + 9 : x = 5, x = - 5, x = 2, x = - 2

x = 5, x = - 5, x = 2, x = - 2

Verify Solutions:

x = 5

True

, x = - 5

True

, x = 2

False

, x = - 2

False

The solutions are

x = 5, x = - 5

x^{2} = - 1

\frac{1}{x} = \frac{1}{3}

9 x + 5 = 11

x^{2} = 25

(2 x + 1)^{\frac{1}{3}} = 4

What is the answer to sqrt(x^2-1)+3=x^2 ?
The answer to sqrt(x^2-1)+3=x^2 is x=sqrt(5),x=-sqrt(5)
Solve for x: sqrt(x^2-1)+3=x^2
The solution is x=sqrt(5),x=-sqrt(5)