What is the answer to (r^2+x^2)^{3/2}=8r^3 ?

The answer to (r^2+x^2)^{3/2}=8r^3 is x=rsqrt(3) {r>= 0},x=-rsqrt(3) {r>= 0}

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(r^2+x^2)^{3/2}=8r^3

(r^{2} + x^{2})^{\frac{3}{2}} = 8 r^{3}

x = r 3 {r \geq 0}, x = - r 3 {r \geq 0}

Solution steps

(r^{2} + x^{2})^{\frac{3}{2}} = 8 r^{3}

Take both sides of the equation to the power of

2 : (r^{2} + x^{2})^{3} = 64 r^{6}

(r^{2} + x^{2})^{3} = 64 r^{6}

Solve

(r^{2} + x^{2})^{3} = 64 r^{6} : x = r 3, x = - r 3

x = r 3, x = - r 3

Verify Solutions:

x = r 3 {r \geq 0}, x = - r 3 {r \geq 0}

The solutions are

x = r 3 {r \geq 0}, x = - r 3 {r \geq 0}

x^{\frac{1}{3}} + 16 = 0

2 x^{2} + 7 x - 7 = 0

\frac{5}{( x ) - x} = x + 2

9 = x^{\frac{1}{3}}

3 y - 2 = 23 + 4

What is the answer to (r^2+x^2)^{3/2}=8r^3 ?
The answer to (r^2+x^2)^{3/2}=8r^3 is x=rsqrt(3) {r>= 0},x=-rsqrt(3) {r>= 0}