Solve 3x^2x^(2)=5

Question

Solve the equation

x_{1} = - \frac{4 135}{3}, x_{2} = \frac{4 135}{3}

Alternative Form

x_{1} \approx - 1.136219, x_{2} \approx 1.136219

Evaluate

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

Multiply

More Steps

Evaluate

3 x^{2} \times x^{2}

Multiply the terms with the same base by adding their exponents

3 x^{2 + 2}

Add the numbers

3 x^{4}

3 x^{4} = 5

Divide both sides

\frac{3 x ^{4}}{3} = \frac{5}{3}

Divide the numbers

x^{4} = \frac{5}{3}

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

x = \pm 4 \frac{5}{3}

Simplify the expression

More Steps

Evaluate

4 \frac{5}{3}

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

\frac{4 5}{4 3}

Multiply by the Conjugate

\frac{4 5 \times 4 3 ^{3}}{4 3 \times 4 3 ^{3}}

Simplify

\frac{4 5 \times 4 27}{4 3 \times 4 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

45 \times 427

The product of roots with the same index is equal to the root of the product

4 5 \times 27

Calculate the product

4135

\frac{4 135}{4 3 \times 4 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

43 \times 4 3^{3}

The product of roots with the same index is equal to the root of the product

4 3 \times 3^{3}

Calculate the product

4 3^{4}

Reduce the index of the radical and exponent with 4

3

\frac{4 135}{3}

x = \pm \frac{4 135}{3}

Separate the equation into 2 possible cases

x = \frac{4 135}{3} x = - \frac{4 135}{3}

Solution

x_{1} = - \frac{4 135}{3}, x_{2} = \frac{4 135}{3}

Alternative Form

x_{1} \approx - 1.136219, x_{2} \approx 1.136219

Show Solution