If = m n , then n 2 +m 2 is equal to

Step-by-step solution

We have, = m n Now, n 2 +m 2 aligned &=n [ 1- ² 1+ ² ]+m [ 2 1+ ² ] &=n [ 1- m² n² 1+ m² n² ]+m [ 2 m n 1+ m² n² ] &=n [ n²-m² n²+m² ]+ [ 2 m² n n² n²+m² ] &=n [ n²-m² m²+n² ]+ 2 m² n n²+m² = n (n²-m² )+2 m² n (m²+n² ) &= n [n²-m²+2 m² ] (m²+n² ) = n (n²+m² ) (m²+n² ) =n aligned