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

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

Popular >

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

expand

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

\frac{3}{2} + \frac{5}{2}

Decimal Notation

2.61803 \dots

Solution steps

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

Apply exponent rule:

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

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

(1 + 5)^{2} = 6 + 25

= \frac{6 + 2 5}{2 ^{2}}

Factor

6 + 25 : 2 (3 + 5)

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

Cancel the common factor:

2

= \frac{3 + 5}{2}

Apply the fraction rule:

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

\frac{3 + 5}{2} = \frac{3}{2} + \frac{5}{2}

= \frac{3}{2} + \frac{5}{2}

\frac{3 x ^{3} - 4 x + 5}{( x - 1 ) ( x ^{2} + 2 x + 1 )}

\frac{2 x ^{2} + x + 8}{( x ^{2} + 4 ) ^{2}}

(1 + y^{2}) d x

\frac{( 3 - 5 + x ) ( 1 + 5 - x )}{x - 4}

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

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