Solve 3*frac{sqrt{5}-1}{2}*frac{sqrt{5}+1}{2}

$$3 \times \frac { \sqrt { 5 } - 1 } { 2 } \times \frac { \sqrt { 5 } + 1 } { 2 }$$

Evaluate

$$3$$

Solution Steps

Express 3\times \frac{\sqrt{5}-1}{2} as a single fraction.

$$\frac{3\left(\sqrt{5}-1\right)}{2}\times \frac{\sqrt{5}+1}{2}$$

Multiply \frac{3\left(\sqrt{5}-1\right)}{2} times \frac{\sqrt{5}+1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{3\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)}{4}$$

Use the distributive property to multiply 3 by \sqrt{5}-1.

$$\frac{\left(3\sqrt{5}-3\right)\left(\sqrt{5}+1\right)}{4}$$

Apply the distributive property by multiplying each term of 3\sqrt{5}-3 by each term of \sqrt{5}+1.

$$\frac{3\left(\sqrt{5}\right)^{2}+3\sqrt{5}-3\sqrt{5}-3}{4}$$

The square of \sqrt{5} is 5.

$$\frac{3\times 5+3\sqrt{5}-3\sqrt{5}-3}{4}$$

Multiply 3 and 5 to get 15.

$$\frac{15+3\sqrt{5}-3\sqrt{5}-3}{4}$$

Combine 3\sqrt{5} and -3\sqrt{5} to get 0.

$$\frac{15-3}{4}$$

Subtract 3 from 15 to get 12.

$$\frac{12}{4}$$

Divide 12 by 4 to get 3.

$$3$$

Factor

$$3$$