What is the answer to x^3-6x^2+9x=sqrt(x) ?

The answer to x^3-6x^2+9x=sqrt(x) is x=0,x\approx 0.01255…,x\approx 2.17671…,x\approx 3.72005…

Solve for x: x^3-6x^2+9x=sqrt(x)

The solution is x=0,x\approx 0.01255…,x\approx 2.17671…,x\approx 3.72005…

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x^{3} - 6 x^{2} + 9 x = x

x = 0, x \approx 0.01255 \dots, x \approx 2.17671 \dots, x \approx 3.72005 \dots

Solution steps

x^{3} - 6 x^{2} + 9 x = x

Square both sides:

x^{6} - 12 x^{5} + 54 x^{4} - 108 x^{3} + 81 x^{2} = x

x^{6} - 12 x^{5} + 54 x^{4} - 108 x^{3} + 81 x^{2} = x

Solve

x^{6} - 12 x^{5} + 54 x^{4} - 108 x^{3} + 81 x^{2} = x : x = 0, x \approx 0.01255 \dots, x \approx 2.17671 \dots, x \approx 3.72005 \dots

x = 0, x \approx 0.01255 \dots, x \approx 2.17671 \dots, x \approx 3.72005 \dots

Verify Solutions:

x = 0

True

, x \approx 0.01255 \dots

True

, x \approx 2.17671 \dots

True

, x \approx 3.72005 \dots

True

The solutions are

x = 0, x \approx 0.01255 \dots, x \approx 2.17671 \dots, x \approx 3.72005 \dots

2 - x - 3 x + 1 = - 1

- 6 - x + x = 0

x + - x = 4

x + 3 = x + 9

2 x + 5 - 2 x = 3

What is the answer to x^3-6x^2+9x=sqrt(x) ?
The answer to x^3-6x^2+9x=sqrt(x) is x=0,x\approx 0.01255…,x\approx 2.17671…,x\approx 3.72005…
Solve for x: x^3-6x^2+9x=sqrt(x)
The solution is x=0,x\approx 0.01255…,x\approx 2.17671…,x\approx 3.72005…