Solve (frac{5-sqrt{17}}{2})^2

$$( \frac { 5 - \sqrt { 17 } } { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{21-5\sqrt{17}}{2}\approx 0.192235936$$

Solution Steps

To raise \frac{5-\sqrt{17}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5-\sqrt{17}\right)^{2}}{2^{2}}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5-\sqrt{17}\right)^{2}.

$$\frac{25-10\sqrt{17}+\left(\sqrt{17}\right)^{2}}{2^{2}}$$

The square of \sqrt{17} is 17.

$$\frac{25-10\sqrt{17}+17}{2^{2}}$$

Add 25 and 17 to get 42.

$$\frac{42-10\sqrt{17}}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{42-10\sqrt{17}}{4}$$

Expand

$$\frac{21 - 5 \sqrt{17}}{2} = 0.1922359359558481$$

Solution Steps

To raise \frac{5-\sqrt{17}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5-\sqrt{17}\right)^{2}}{2^{2}}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5-\sqrt{17}\right)^{2}.

$$\frac{25-10\sqrt{17}+\left(\sqrt{17}\right)^{2}}{2^{2}}$$

The square of \sqrt{17} is 17.

$$\frac{25-10\sqrt{17}+17}{2^{2}}$$

Add 25 and 17 to get 42.

$$\frac{42-10\sqrt{17}}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{42-10\sqrt{17}}{4}$$