Solve frac{(sqrt{5}+1)*(sqrt{5}-1)}{2*2}

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

Evaluate

$$1$$

Solution Steps

Consider \left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

The square of \sqrt{5} is 5.

$$\frac{5-1^{2}}{2\times 2}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{5-1}{2\times 2}$$

Subtract 1 from 5 to get 4.

$$\frac{4}{2\times 2}$$

Multiply 2 and 2 to get 4.

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

Divide 4 by 4 to get 1.

$$1$$

Factor

$$1$$