Solve frac{sqrt{5}+1}{2}frac{-sqrt{5}-1}{2}

$$\frac{ \sqrt{ 5 } +1 }{ 2 } \frac{ - \sqrt{ 5 } -1 }{ 2 }$$

Evaluate

$$\frac{-\sqrt{5}-3}{2}\approx -2.618033989$$

Solution Steps

Multiply \frac{\sqrt{5}+1}{2} times \frac{-\sqrt{5}-1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(\sqrt{5}+1\right)\left(-\sqrt{5}-1\right)}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{\left(\sqrt{5}+1\right)\left(-\sqrt{5}-1\right)}{4}$$

Apply the distributive property by multiplying each term of \sqrt{5}+1 by each term of -\sqrt{5}-1.

$$\frac{-\left(\sqrt{5}\right)^{2}-\sqrt{5}-\sqrt{5}-1}{4}$$

The square of \sqrt{5} is 5.

$$\frac{-5-\sqrt{5}-\sqrt{5}-1}{4}$$

Combine -\sqrt{5} and -\sqrt{5} to get -2\sqrt{5}.

$$\frac{-5-2\sqrt{5}-1}{4}$$

Subtract 1 from -5 to get -6.

$$\frac{-6-2\sqrt{5}}{4}$$

Factor

$$\frac{-\sqrt{5} - 3}{2} = -2.618033988749895$$