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

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

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

The solution is x=2sqrt(2),x=-2sqrt(2)

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

x = 22, x = - 22

Decimal Notation

x = 2.82842 \dots, x = - 2.82842 \dots

Solution steps

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

Square both sides:

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

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

Solve

x^{4} - 10 x^{2} + 25 = 1 + x^{2} : x = 22, x = - 22, x = 3, x = - 3

x = 22, x = - 22, x = 3, x = - 3

Verify Solutions:

x = 22

True

, x = - 22

True

, x = 3

False

, x = - 3

False

The solutions are

x = 22, x = - 22

x + 28 - x - 4 = 4

2 x - \frac{54}{x} = 0

3 t + 6 = - 6

x^{\frac{5}{7}} = 243

3 y + 37 + 7 = y + 6

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