Solve 121u^2 121u^2 - 121*11

Question

Simplify the expression

14641 u^{4} - 1331

Evaluate

121 u^{2} \times 121 u^{2} - 121 \times 11

Multiply

More Steps

Multiply the terms

121 u^{2} \times 121 u^{2}

Multiply the terms

14641 u^{2} \times u^{2}

Multiply the terms with the same base by adding their exponents

14641 u^{2 + 2}

Add the numbers

14641 u^{4}

14641 u^{4} - 121 \times 11

Solution

14641 u^{4} - 1331

Show Solution

Factor the expression

1331 (11 u^{4} - 1)

Evaluate

121 u^{2} \times 121 u^{2} - 121 \times 11

Multiply

More Steps

Multiply the terms

121 u^{2} \times 121 u^{2}

Multiply the terms

14641 u^{2} \times u^{2}

Multiply the terms with the same base by adding their exponents

14641 u^{2 + 2}

Add the numbers

14641 u^{4}

14641 u^{4} - 121 \times 11

Multiply the numbers

14641 u^{4} - 1331

Solution

1331 (11 u^{4} - 1)

Show Solution

Find the roots

u_{1} = - \frac{4 1331}{11}, u_{2} = \frac{4 1331}{11}

Alternative Form

u_{1} \approx - 0.5491, u_{2} \approx 0.5491

Evaluate

121 u^{2} \times 121 u^{2} - 121 \times 11

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

121 u^{2} \times 121 u^{2} - 121 \times 11 = 0

Multiply

More Steps

Multiply the terms

121 u^{2} \times 121 u^{2}

Multiply the terms

14641 u^{2} \times u^{2}

Multiply the terms with the same base by adding their exponents

14641 u^{2 + 2}

Add the numbers

14641 u^{4}

14641 u^{4} - 121 \times 11 = 0

Multiply the numbers

14641 u^{4} - 1331 = 0

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

14641 u^{4} = 0 + 1331

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

14641 u^{4} = 1331

Divide both sides

\frac{14641 u ^{4}}{14641} = \frac{1331}{14641}

Divide the numbers

u^{4} = \frac{1331}{14641}

Cancel out the common factor 1331

u^{4} = \frac{1}{11}

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

u = \pm 4 \frac{1}{11}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{11}

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

\frac{4 1}{4 11}

Simplify the radical expression

\frac{1}{4 11}

Multiply by the Conjugate

\frac{4 1 1 ^{3}}{4 11 \times 4 1 1 ^{3}}

Simplify

\frac{4 1331}{4 11 \times 4 1 1 ^{3}}

Multiply the numbers

More Steps

Evaluate

411 \times 4 1 1^{3}

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

4 11 \times 1 1^{3}

Calculate the product

4 1 1^{4}

Reduce the index of the radical and exponent with 4

11

\frac{4 1331}{11}

u = \pm \frac{4 1331}{11}

Separate the equation into 2 possible cases

u = \frac{4 1331}{11} u = - \frac{4 1331}{11}

Solution

u_{1} = - \frac{4 1331}{11}, u_{2} = \frac{4 1331}{11}

Alternative Form

u_{1} \approx - 0.5491, u_{2} \approx 0.5491

Show Solution