Solve (x^(4)-3x^( 1/3 ))^(2)

Question

Simplify the expression

x^{8} - 6 3 x \times x^{4} + 9 3 x^{2}

Evaluate

(x^{4} - 3 x^{\frac{1}{3}})^{2}

Use a^{\frac{m}{n}} = n a^{m} to transform the expression

(x^{4} - 3 3 x)^{2}

Solution

More Steps

Use the the distributive property to expand the expression

x^{4} \times x^{4} + x^{4} (- 3 3 x) - 3 3 x \times x^{4} - 3 3 x \times (- 3 3 x)

Multiply the terms

More Steps

Evaluate

x^{4} \times x^{4}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{4 + 4}

Add the numbers

x^{8}

x^{8} + x^{4} (- 3 3 x) - 3 3 x \times x^{4} - 3 3 x \times (- 3 3 x)

Multiply the terms

More Steps

Evaluate

x^{4} (- 3 3 x)

Rewrite the expression

- x^{4} \times 3 3 x

Use the commutative property to reorder the terms

- 3 x^{4} 3 x

x^{8} - 3 x^{4} 3 x - 3 3 x \times x^{4} - 3 3 x \times (- 3 3 x)

Multiply the terms

More Steps

Evaluate

- 3 3 x \times (- 3 3 x)

Calculate

- 3 (- 3 3 x^{2})

Rewrite the expression

3 \times 3 3 x^{2}

Multiply the terms

9 3 x^{2}

x^{8} - 3 x^{4} 3 x - 3 3 x \times x^{4} + 9 3 x^{2}

Calculate

More Steps

Evaluate

- 3 x^{4} 3 x - 3 3 x \times x^{4}

Rewrite the expression

- 3 3 x \times x^{4} - 3 3 x \times x^{4}

Collect like terms by calculating the sum or difference of their coefficients

(- 3 - 3) 3 x \times x^{4}

Subtract the numbers

- 6 3 x \times x^{4}

x^{8} - 6 3 x \times x^{4} + 9 3 x^{2}

x^{8} - 6 3 x \times x^{4} + 9 3 x^{2}

Show Solution

x_{1} = 0, x_{2} = 1127

Alternative Form

x_{1} = 0, x_{2} \approx 1.349348

Evaluate

(x^{4} - 3 x^{\frac{1}{3}})^{2}

To find the roots of the expression,set the expression equal to 0

(x^{4} - 3 x^{\frac{1}{3}})^{2} = 0

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

x^{4} - 3 x^{\frac{1}{3}} = 0

Factor the expression

x^{\frac{1}{3}} (x^{\frac{11}{3}} - 3) = 0

Separate the equation into 2 possible cases

x^{\frac{1}{3}} = 0 x^{\frac{11}{3}} - 3 = 0

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

x = 0 x^{\frac{11}{3}} - 3 = 0

Solve the equation

More Steps

Evaluate

x^{\frac{11}{3}} - 3 = 0

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

x^{\frac{11}{3}} = 0 + 3

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

x^{\frac{11}{3}} = 3

Raise both sides of the equation to the reciprocal of the exponent

(x^{\frac{11}{3}})^{\frac{3}{11}} = 3^{\frac{3}{11}}

Calculate

x = 11 3^{3}

Simplify

x = 1127

x = 0 x = 1127

Solution

x_{1} = 0, x_{2} = 1127

Alternative Form

x_{1} = 0, x_{2} \approx 1.349348

Show Solution