What is (x+((1+sqrt(5)))/2)(x+((1-sqrt(5)))/2) ?

The solution to (x+((1+sqrt(5)))/2)(x+((1-sqrt(5)))/2) is x^2+x-1

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simplify (x+((1+sqrt(5)))/2)(x+((1-sqrt(5)))/2)

simplify

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

x^{2} + x - 1

Solution steps

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

Simplify

x + \frac{1 + 5}{2} : \frac{2 x + 1 + 5}{2}

= \frac{2 x + 1 + 5}{2} (x + \frac{1 - 5}{2})

Apply the fraction rule:

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

= \frac{( 2 x + 1 + 5 ) ( x + \frac{1 - 5}{2} )}{2}

Simplify

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

= \frac{2 x ^{2} + 2 x - 2}{2}

Factor

2 x^{2} + 2 x - 2 : 2 (x^{2} + x - 1)

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

Cancel the common factor:

2

= x^{2} + x - 1

(4 - x) ln (x + 4)

ln (x) (e^{x} v_{1} + \frac{e ^{x}}{x} v_{2} = 0)

(- 2 y + 8 + 2)^{2}

(4 y - 5 i)^{2}

\frac{e ^{- 2 s}}{( s ^{2} + 9 ) ( s ^{2} + 1 )}

What is (x+((1+sqrt(5)))/2)(x+((1-sqrt(5)))/2) ?
The solution to (x+((1+sqrt(5)))/2)(x+((1-sqrt(5)))/2) is x^2+x-1