Solve 5/3 y^5=5y^3/2

Question

Solve the equation

y_{1} = - \frac{6}{2}, y_{2} = 0, y_{3} = \frac{6}{2}

Alternative Form

y_{1} \approx - 1.224745, y_{2} = 0, y_{3} \approx 1.224745

Evaluate

\frac{5}{3} y^{5} = 5 \times \frac{y ^{3}}{2}

Multiply the terms

\frac{5}{3} y^{5} = \frac{5 y ^{3}}{2}

Rewrite the expression

\frac{5 y ^{5}}{3} = \frac{5 y ^{3}}{2}

Cross multiply

5 y^{5} \times 2 = 3 \times 5 y^{3}

Simplify the equation

10 y^{5} = 3 \times 5 y^{3}

Simplify the equation

10 y^{5} = 15 y^{3}

Rewrite the expression

5 \times 2 y^{5} = 5 \times 3 y^{3}

Evaluate

2 y^{5} = 3 y^{3}

Add or subtract both sides

2 y^{5} - 3 y^{3} = 0

Factor the expression

y^{3} (2 y^{2} - 3) = 0

Separate the equation into 2 possible cases

y^{3} = 0 2 y^{2} - 3 = 0

The only way a power can be 0 is when the base equals 0

y = 0 2 y^{2} - 3 = 0

Solve the equation

More Steps

Evaluate

2 y^{2} - 3 = 0

Move the constant to the right-hand side and change its sign

2 y^{2} = 0 + 3

Removing 0 doesn't change the value,so remove it from the expression

2 y^{2} = 3

Divide both sides

\frac{2 y ^{2}}{2} = \frac{3}{2}

Divide the numbers

y^{2} = \frac{3}{2}

Take the root of both sides of the equation and remember to use both positive and negative roots

y = \pm \frac{3}{2}

Simplify the expression

More Steps

Evaluate

\frac{3}{2}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3}{2}

Multiply by the Conjugate

\frac{3 \times 2}{2 \times 2}

Multiply the numbers

\frac{6}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{6}{2}

y = \pm \frac{6}{2}

Separate the equation into 2 possible cases

y = \frac{6}{2} y = - \frac{6}{2}

y = 0 y = \frac{6}{2} y = - \frac{6}{2}

Solution

y_{1} = - \frac{6}{2}, y_{2} = 0, y_{3} = \frac{6}{2}

Alternative Form

y_{1} \approx - 1.224745, y_{2} = 0, y_{3} \approx 1.224745

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