What is the answer to sqrt(x^2-1)=x^2-5 ?

The answer to sqrt(x^2-1)=x^2-5 is x=sqrt((11+\sqrt{17))/2},x=-sqrt((11+\sqrt{17))/2}

Solve for x: sqrt(x^2-1)=x^2-5

The solution is x=sqrt((11+\sqrt{17))/2},x=-sqrt((11+\sqrt{17))/2}

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x^{2} - 1 = x^{2} - 5

x = \frac{11 + 17}{2}, x = - \frac{11 + 17}{2}

Decimal

x = 2.74982 \dots, x = - 2.74982 \dots

Solution steps

x^{2} - 1 = x^{2} - 5

Square both sides:

x^{2} - 1 = x^{4} - 10 x^{2} + 25

x^{2} - 1 = x^{4} - 10 x^{2} + 25

Solve

x^{2} - 1 = x^{4} - 10 x^{2} + 25 : x = \frac{11 + 17}{2}, x = - \frac{11 + 17}{2}, x = \frac{11 - 17}{2}, x = - \frac{11 - 17}{2}

x = \frac{11 + 17}{2}, x = - \frac{11 + 17}{2}, x = \frac{11 - 17}{2}, x = - \frac{11 - 17}{2}

Verify Solutions:

x = \frac{11 + 17}{2}

True

, x = - \frac{11 + 17}{2}

True

, x = \frac{11 - 17}{2}

False

, x = - \frac{11 - 17}{2}

False

The solutions are

x = \frac{11 + 17}{2}, x = - \frac{11 + 17}{2}

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

x - 3 - 2 x = - 6

y, y^{\frac{1}{3}} = x

2 x + 6 x^{2} + 1 = x + 1

x^{\frac{2}{3}} - 3 x^{\frac{1}{3}} - 18 = 0

What is the answer to sqrt(x^2-1)=x^2-5 ?
The answer to sqrt(x^2-1)=x^2-5 is x=sqrt((11+\sqrt{17))/2},x=-sqrt((11+\sqrt{17))/2}
Solve for x: sqrt(x^2-1)=x^2-5
The solution is x=sqrt((11+\sqrt{17))/2},x=-sqrt((11+\sqrt{17))/2}