Question

If MX+NY=m+n, then prove that m(1/m-n-1/m+n) x+n(1/n-m-1/m+n) y=2m/m+n

Answer 1

Let mx − ny = m2 + n2  → (1)
         x − y =  2n
Multiply above equation with n, we get
nx − ny = 2n2  → (2)
subtract (2) from (1)
mx − ny = m2 + n2
nx − ny = 2n2  
−     +      −    
(m − n)x = m2 − n2
⇒ (m − n)x = (m − n)(m + n)
∴ x = (m + n)
Put x = (m + n) in   x − y =  2n
⇒ (m + n) − y =  2n
⇒ (m + n) − 2n =  y
∴ y = (m − n)

Let mx − ny = m2 + n2  → (1)
         x − y =  2n
Multiply above equation with n, we get
nx − ny = 2n2  → (2)
subtract (2) from (1)
mx − ny = m2 + n2
nx − ny = 2n2  
−     +      −    
(m − n)x = m2 − n2
⇒ (m − n)x = (m − n)(m + n)
∴ x = (m + n)
Put x = (m + n) in   x − y =  2n
⇒ (m + n) − y =  2n
⇒ (m + n) − 2n =  y
∴ y = (m − n)