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

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

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

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 + 9) - 3 = x

x + 18 - x - 10 = 2

2 x - 5 = 43

50 = 3 y + 5 y

x - 7 - 1 - 2 x = 10

What is the answer to solvefor x,sqrt(3x-1)=x^2-x ?
The answer to solvefor x,sqrt(3x-1)=x^2-x is x\approx 2.09692…