What is expand ((1+sqrt(5))/2)^3 ?

The solution to expand ((1+sqrt(5))/2)^3 is 2+sqrt(5)

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expand ((1+sqrt(5))/2)^3

expand

(\frac{1 + 5}{2})^{3}

2 + 5

Decimal Notation

4.23606 \dots

Solution steps

(\frac{1 + 5}{2})^{3}

Apply exponent rule:

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

= \frac{( 1 + 5 ) ^{3}}{2 ^{3}}

(1 + 5)^{3} = 16 + 85

= \frac{16 + 8 5}{2 ^{3}}

Factor

16 + 85 : 8 (2 + 5)

= \frac{8 ( 2 + 5 )}{2 ^{3}}

Factor

8 : 2^{3}

= \frac{2 ^{3} ( 2 + 5 )}{2 ^{3}}

Cancel the common factor:

2^{3}

= 2 + 5

3 (\frac{3 e ^{- t} t ^{2}}{2} - 6 e^{- t} t + 3 e^{- t})

\frac{e ^{- x} - x ^{2} - x + 10}{( x - 1 ) ( x + 4 ) ( x - 2 )}

(x + sin (\frac{π \cdot x}{2})) \cdot (x + cos (\frac{π \cdot x}{2}))^{2}

\frac{10 ( 3 191 - 2 )}{49}

lo g_{10} (y)

What is expand ((1+sqrt(5))/2)^3 ?
The solution to expand ((1+sqrt(5))/2)^3 is 2+sqrt(5)