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If M ≠ N and (M + N)-1 (M-1 + N-1) = Mxny, Show that : X + Y + 2 = 0 - Mathematics

Sum

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

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Solution

(m + n)-1 (m-1 + n-1) = mxny

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

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

⇒ `1/(mn) = m^x.n^y`

⇒ `m^-1n^-1 = m^x.n^y`
Comparing the coefficient of x and y, we get
x = - 1 and y = -1
LHS
y + y + 2 = ( - 1) + ( - 1) + 2 = 0 = RHS

Concept: Solving Exponential Equations
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (B) | Q 11 | Page 101
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