Solve quadtext{If}N=frac{sqrt{sqrt{5}+2}+sqrt{sqrt{5}-2}}{sqrt{sqrt{5}+1}}-sqrt{3-2sqrt{2}}

$$\quad \text { If } N = \frac { \sqrt { \sqrt { 5 } + 2 } + \sqrt { \sqrt { 5 } - 2 } } { \sqrt { \sqrt { 5 } + 1 } } - \sqrt { 3 - 2 \sqrt { 2 } }$$

Solve for I

$$I=\frac{1}{Nf}$$

$$N\neq 0\text{ and }f\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

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

Divide both sides by fN.

$$\frac{NfI}{Nf}=\frac{\sqrt{\sqrt{5}-1}\left(-\left(\sqrt{2}-1\right)\sqrt{\sqrt{5}+1}+\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}\right)}{2Nf}$$

Dividing by fN undoes the multiplication by fN.

$$I=\frac{\sqrt{\sqrt{5}-1}\left(-\left(\sqrt{2}-1\right)\sqrt{\sqrt{5}+1}+\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}\right)}{2Nf}$$

Divide \frac{\left(-\left(\sqrt{2}-1\right)\sqrt{\sqrt{5}+1}+\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}\right)\sqrt{\sqrt{5}-1}}{2} by fN.

$$I=\frac{\sqrt{\sqrt{5}-1}\left(\sqrt{\sqrt{5}+1}+\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}-\sqrt{2\sqrt{5}+2}\right)}{2Nf}$$

Solve for N

$$N=\frac{1}{If}$$

$$f\neq 0\text{ and }I\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

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

Divide both sides by If.

$$\frac{IfN}{If}=\frac{\sqrt{\sqrt{5}-1}\left(-\left(\sqrt{2}-1\right)\sqrt{\sqrt{5}+1}+\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}\right)}{2If}$$

Dividing by If undoes the multiplication by If.

$$N=\frac{\sqrt{\sqrt{5}-1}\left(-\left(\sqrt{2}-1\right)\sqrt{\sqrt{5}+1}+\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}\right)}{2If}$$

Divide \frac{\left(-\left(\sqrt{2}-1\right)\sqrt{\sqrt{5}+1}+\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}\right)\sqrt{\sqrt{5}-1}}{2} by If.

$$N=\frac{\sqrt{\sqrt{5}-1}\left(\sqrt{\sqrt{5}+1}+\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}-\sqrt{2\sqrt{5}+2}\right)}{2If}$$