What is the answer to solvefor y,y+sqrt(yx)=3x^3 ?

The answer to solvefor y,y+sqrt(yx)=3x^3 is y=(6x^3+x+xsqrt(12x^2+1))/2 ,y=(6x^3+x-xsqrt(12x^2+1))/2

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solvefor y,y+sqrt(yx)=3x^3

solve for

y, y + y x = 3 x^{3}

y = \frac{6 x ^{3} + x + x 12 x ^{2} + 1}{2}, y = \frac{6 x ^{3} + x - x 12 x ^{2} + 1}{2}

Solution steps

y + y x = 3 x^{3}

Remove square roots

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

Solve

y x = 9 x^{6} - 6 y x^{3} + y^{2} : y = \frac{6 x ^{3} + x + x 12 x ^{2} + 1}{2}, y = \frac{6 x ^{3} + x - x 12 x ^{2} + 1}{2}

y = \frac{6 x ^{3} + x + x 12 x ^{2} + 1}{2}, y = \frac{6 x ^{3} + x - x 12 x ^{2} + 1}{2}

Verify Solutions:

y = \frac{6 x ^{3} + x + x 12 x ^{2} + 1}{2}

True

, y = \frac{6 x ^{3} + x - x 12 x ^{2} + 1}{2}

True

The solutions are

y = \frac{6 x ^{3} + x + x 12 x ^{2} + 1}{2}, y = \frac{6 x ^{3} + x - x 12 x ^{2} + 1}{2}

x^{2} + 19 x - 18 = 4 x + 2

y, x + y = 8

y, x^{\frac{2}{3}} + y^{\frac{2}{3}} = 5

4 w + 4 = - 4

- 2 x^{\frac{3}{4}} + 47 = - 7

What is the answer to solvefor y,y+sqrt(yx)=3x^3 ?
The answer to solvefor y,y+sqrt(yx)=3x^3 is y=(6x^3+x+xsqrt(12x^2+1))/2 ,y=(6x^3+x-xsqrt(12x^2+1))/2