If m- n and m-n-1m-1-n-1-mxny- show that -x-y-2-0

(m + n)^ 1 (m^ 1 + n^ 1) = m^x n^y L.H.S. = 1m+n(1m + 1n) = ( 1m+n) (n+mnm) = 1nm = m^ 1n^ 1 R.H.S = m^xn^y ⇒ x = 1 & y = 1 ...

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Standard X

Mathematics

GCD of Polynomials

If m≠ n and...

Question

If $m \neq n$ and $(m + n)^{- 1} (m^{- 1} + n^{- 1}) = m^{x} n^{y}$ ; show that $: x + y + 2 = 0$

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Solution

$(m + n)^{- 1} (m^{- 1} + n^{- 1}) = m^{x} n^{y}$
L.H.S.
$= \frac{1}{m + n} (\frac{1}{m} + \frac{1}{n})$
$= (\frac{1}{m + n}) (\frac{n + m}{n m})$
$= \frac{1}{n m} = m^{- 1} n^{- 1}$
R.H.S $= m^{x} n^{y}$
$\Rightarrow x = - 1 & y = 1$
$\Rightarrow x + y + 2 = (- 1) + (- 1) + 2 = 0$

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

(m+n)−1(m−1+n−1)=mxnyL.H.S.=1m+n(1m+1n)=(1m+n)(n+mnm)=1nm=m−1n−1R.H.S =mxny⇒x=−1&y=1⇒x+y+2=(−1)+(−1)+2=0

If $m \neq n$ and $(m + n)^{- 1} (m^{- 1} + n^{- 1}) = m^{x} n^{y}$ ; show that $: x + y + 2 = 0$

$(m + n)^{- 1} (m^{- 1} + n^{- 1}) = m^{x} n^{y}$
L.H.S.
$= \frac{1}{m + n} (\frac{1}{m} + \frac{1}{n})$
$= (\frac{1}{m + n}) (\frac{n + m}{n m})$
$= \frac{1}{n m} = m^{- 1} n^{- 1}$
R.H.S $= m^{x} n^{y}$
$\Rightarrow x = - 1 & y = 1$
$\Rightarrow x + y + 2 = (- 1) + (- 1) + 2 = 0$