Question
Solve the system of equations
(x,y,z)=(32×z,3336×z,z),z∈R
Alternative Form
Infinitely many solutions
Evaluate
{2x3=3y33y3=4z3
Solve the equation for x
More Steps

Evaluate
2x3=3y3
Divide both sides
22x3=23y3
Divide the numbers
x3=23y3
Take the 3-th root on both sides of the equation
3x3=323y3
Calculate
x=323y3
Simplify the root
More Steps

Evaluate
323y3
To take a root of a fraction,take the root of the numerator and denominator separately
3233y3
Multiply by the Conjugate
32×32233y3×322
Calculate
233y3×322
Calculate
2312×y
x=2312×y
{x=2312×y3y3=4z3
Substitute the given value of x into the equation 3y3=4z3
3y3=4z3
Divide both sides
33y3=34z3
Divide the numbers
y3=34z3
Take the 3-th root on both sides of the equation
3y3=334z3
Calculate
y=334z3
Simplify the root
More Steps

Evaluate
334z3
To take a root of a fraction,take the root of the numerator and denominator separately
3334z3
Multiply by the Conjugate
33×33234z3×332
Calculate
334z3×332
Calculate
More Steps

Evaluate
34z3×332
The product of roots with the same index is equal to the root of the product
34z3×32
Calculate the product
336z3
Reorder the terms
3z3×36
The root of a product is equal to the product of the roots of each factor
3z3×336
Reduce the index of the radical and exponent with 3
336×z
3336×z
y=3336×z
Substitute the given value of y into the equation x=2312×y
x=2312×3336×z
Simplify the expression
x=32×z
Solution
(x,y,z)=(32×z,3336×z,z),z∈R
Alternative Form
Infinitely many solutions
Show Solution
