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Cube root equations

Solve the first problem 18 problems

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1. Cube root plus square root equation ●●○○○ 20 ptsSolve the equation $\sqrt[3]{x} + \sqrt{x+12} = 0$ for $x$.
2. Equation with square and cube roots ●●○○○ 20 ptsSolve the equation $\frac{\sqrt{x}+\sqrt[3]{x}}{\sqrt{x}-\sqrt[3]{x}}=3$ for real $x$.
3. Fractional-power equation with substitution ●●○○○ 20 ptsSolve the equation $(x - 2)^{2/3} + (x - 2)^{1/3} - 2 = 0$, using real cube roots.
4. Cube root equation for x to the sixth ●●●○○ 50 ptsA positive real number $x$ satisfies $\sqrt[3]{1-x^3} + \sqrt[3]{1+x^3} = 1$. Find $x^6$. Round to two decimal places.
5. Radical equation with cube roots ●●●○○ 50 ptsSolve the equation $\sqrt[3]{9-\sqrt{x+1}}+\sqrt[3]{7+\sqrt{x+1}}=4$.
6. Equation with cube roots ●●●○○ 50 ptsSolve the equation $\sqrt[3]{2x+1}+\sqrt[3]{4-x}=-\sqrt[3]{3}$ for $x$.
7. Exponential equation with a cube root ●●●●○ 100 ptsSolve the equation $27^{x}-7 \sqrt[3]{7 \cdot 3^{x}+6}=6$.
8. Solving an equation with cube roots ●●●●○ 100 ptsFind all real solutions to $\sqrt[3]{15x - 1} + \sqrt[3]{13x + 1} = 4 \sqrt[3]{x}$. Round each solution to two decimal places.

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