Question

if m is not equal to n and (m+n)^-1(m^-1+n^-1) = m^x × n^y show that x+y+2=0​

Answer 1

Answer:

Step-by-step explanation:

(m+n)^-1(m^-1+n^-1) = m^x × n^y

=> 1/(m+n)(1/m + 1/n) = m^x × n^y

=> 1/(m+n)( m+n/mn) =m^x × n^y

=> 1/mn = m^x × n^y

=> m⁻¹n⁻¹ = m^x × n^y

When bases are same, powers are equal.

Thus m⁻¹ = m^x  => x = -1.

        n⁻¹ =  n^y => y = -1.

Substituting the values of x and y in the equation x + y + 2

=> -1 + (-1) + 2

=> -2  + 2

=> 0 = R.H.S

Hence proved