Problem: If $a-\frac{1}{a} =m$ , prove that $a^{4}+\frac{1}{a^{4}}=m^{4}+4m^{2}+2$
View all: BASIC BANK | ASSISTANT OFFICER | WRITTEN QUESTION SOLVE (MATH) | 2009
Correct Answer: See explanation
Explanation:
Given, $a-\frac{1}{a} =m$
=> $(a-\frac{1}{a})^{2} =m^{2}$
=> $a^{2}-2a\frac{1}{a}+(\frac{1}{a})^{2} =m^{2}$
=> $a^{2}+(\frac{1}{a})^{2} =m^{2}+2$
=> $(a^{2}+\frac{1}{a^{2}})^{2} =(m^{2}+2)^{2}$
=> $((a^{2})^{2}+2 a^{2}\frac{1}{a^{2}}+(\frac{1}{a^{2}})^{2} =m^{4}+2m^{2}2+2^{2}$
=> $a^{4}+\frac{1}{a^{4}}=m^{4}+4m^{2}+2$
