Question

If m ≠ n and (m + n)^-1 (m^-1 + n^-1) = m^xn^y, show that : x + y + 2 = 0

Answer 1

(m + n)^-1 (m^-1 + n^-1) = m^xn^y

⇒ `1/( m + n ) xx ( 1/m + 1/n ) = m^x.n^y `

⇒ `1/( cancel(m + n) ) xx ((cancel(m + n))/(mn)) = m^x.n^y `

⇒ `1/(mn) = m^x.n^y`

⇒ `1/m xx 1/n = m^x.n^y`

⇒ `m^-1.n^-1 = m^x.n^y`

Comparing the coefficient of x and y, we get

x = - 1 and y = -1

Putting x = -1 and y = -1

x + y + 2

-1 + (- 1) + 2

- 1 - 1 + 2 = 0 L.H.S