If $$a+ \frac{1}{a}=12$$​, then find the value of $$a^{2}+ \frac{1}{a^{2}}$$​.

Correct option is C

Given:​$$a+ \frac{1}{a}=12$$​​

Formula Used:

​$$(a+b)^{2} = a^{2}+b^{2} + 2ab$$​​

Solution:

​$$a+ \frac{1}{a}=12$$​​

Squaring both sides:

​$$(a+ \frac{1}{a})^{2}=12^{2}$$​​

​$$a^{2}+ \frac{1}{a^{2}}+2(a)( \frac{1}{a})=144$$​​

​$$a^{2}+ \frac{1}{a^{2}}+2 =144$$​​

​$$a^{2}+ \frac{1}{a^{2}} =144-2 = 142$$​​