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प्रश्न
If m ≠ n and (m + n)-1 (m-1 + n-1) = mxny, show that : x + y + 2 = 0
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उत्तर
(m + n)-1 (m-1 + n-1) = mxny
⇒ `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
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