Solve 2x^3=3y^3=4z^3

Evaluate

{2 x^{3} = 3 y^{3} 3 y^{3} = 4 z^{3}

Solve the equation for x

More Steps

{x = \frac{3 12 \times y}{2} 3 y^{3} = 4 z^{3}

Substitute the given value of x into the equation 3 y^{3} = 4 z^{3}

3 y^{3} = 4 z^{3}

Divide both sides

\frac{3 y ^{3}}{3} = \frac{4 z ^{3}}{3}

Divide the numbers

y^{3} = \frac{4 z ^{3}}{3}

Take the 3 -th root on both sides of the equation

3 y^{3} = 3 \frac{4 z ^{3}}{3}

Calculate

y = 3 \frac{4 z ^{3}}{3}

Simplify the root

More Steps

y = \frac{3 36 \times z}{3}

Substitute the given value of y into the equation x = \frac{3 12 \times y}{2}

x = \frac{3 12 \times \frac{3 36 \times z}{3}}{2}

Simplify the expression

x = 32 \times z

Solution

(x, y, z) = (32 \times z, \frac{3 36 \times z}{3}, z), z \in R

Alternative Form

Infinitely many solutions

Solve the system of equations