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

The answer to sqrt(x^2+2)=2x-1 is x=(2+sqrt(7))/3

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

The solution is x=(2+sqrt(7))/3

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

x = \frac{2 + 7}{3}

Decimal Notation

x = 1.54858 \dots

Solution steps

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

Square both sides:

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

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

Solve

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

x = \frac{2 + 7}{3}, x = \frac{2 - 7}{3}

Verify Solutions:

x = \frac{2 + 7}{3}

True

, x = \frac{2 - 7}{3}

False

The solution is

x = \frac{2 + 7}{3}

3 + x = 6 x + 13

0 = - 2 + 1 - x

d, a b^{0.5} = c d^{0.5}

x, - 2 - x + 3 = 0

What is the answer to sqrt(x^2+2)=2x-1 ?
The answer to sqrt(x^2+2)=2x-1 is x=(2+sqrt(7))/3
Solve for x: sqrt(x^2+2)=2x-1
The solution is x=(2+sqrt(7))/3