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

The answer to sqrt(3x-1)=x^2-x is x\approx 2.09692…

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

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

x \approx 2.09692 \dots

Solution steps

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

Square both sides:

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

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

Solve

3 x - 1 = x^{4} - 2 x^{3} + x^{2} : x \approx 0.35061 \dots, x \approx 2.09692 \dots

x \approx 0.35061 \dots, x \approx 2.09692 \dots

Verify Solutions:

x \approx 0.35061 \dots

False

, x \approx 2.09692 \dots

True

The solution is

x \approx 2.09692 \dots

3 x + 19 = x + 5

x - 6 = 19 x + 36

(x + 5)^{2} = x + 5

y, x = 2 y - y^{2}

x - 5 = 23 - x

What is the answer to sqrt(3x-1)=x^2-x ?
The answer to sqrt(3x-1)=x^2-x is x\approx 2.09692…
Solve for x: sqrt(3x-1)=x^2-x
The solution is x\approx 2.09692…