What is expand (((-1-sqrt(41)))/2)^4 ?

The solution to expand (((-1-sqrt(41)))/2)^4 is 241/2+(21sqrt(41))/2

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expand (((-1-sqrt(41)))/2)^4

expand

(\frac{( - 1 - 41 )}{2})^{4}

\frac{241}{2} + \frac{21 41}{2}

Solution steps

(\frac{- 1 - 41}{2})^{4}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( - 1 - 41 ) ^{4}}{2 ^{4}}

(- 1 - 41)^{4} = 1928 + 16841

= \frac{1928 + 168 41}{2 ^{4}}

Factor

1928 + 16841 : 8 (241 + 2141)

= \frac{8 ( 241 + 21 41 )}{2 ^{4}}

Factor

8 : 2^{3}

= \frac{2 ^{3} ( 241 + 21 41 )}{2 ^{4}}

Cancel

\frac{2 ^{3} ( 241 + 21 41 )}{2 ^{4}} : \frac{241 + 21 41}{2}

= \frac{241 + 21 41}{2}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{241 + 21 41}{2} = \frac{241}{2} + \frac{21 41}{2}

= \frac{241}{2} + \frac{21 41}{2}

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What is expand (((-1-sqrt(41)))/2)^4 ?
The solution to expand (((-1-sqrt(41)))/2)^4 is 241/2+(21sqrt(41))/2