Write as a Set of Linear Factors (x-1)^(2/3)=121

${(x - 1)}^{\frac{2}{3}} = 121$

Step 1

Subtract $121$ from both sides of the equation.

${(x - 1)}^{\frac{2}{3}} - 121 = 0$

Step 2

Rewrite ${(x - 1)}^{\frac{2}{3}}$ as ${({(x - 1)}^{\frac{1}{3}})}^{2}$ .

${({(x - 1)}^{\frac{1}{3}})}^{2} - 121 = 0$

Step 3

Rewrite $121$ as $11^{2}$ .

${({(x - 1)}^{\frac{1}{3}})}^{2} - 11^{2} = 0$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = {(x - 1)}^{\frac{1}{3}}$ and $b = 11$ .

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

Write as a Set of Linear Factors (x-1)^(2/3)=121

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