How many pairs of positive integers n- m with n- m satisfy the equation 1-5-1-n-1-m-

The correct option is C 2 1 / m + 1 / n =5. #160; 5× m+5× n=mn. (n 5)× (m 5)=25 #160; (n 5)× (m 5)=1× 25 or 5× 5 or 25× ...

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Standard XII

Mathematics

Equality of Matrices

How many pair...

Question

How many pairs of positive integers $(n . m)$ with $n \leq m$ satisfy the equation $\frac{1}{5} = \frac{1}{n} + \frac{1}{m}$ ?

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Solution

The correct option is C $2$
$\frac{1}{m} + \frac{1}{n} = 5.$
$5 \times m + 5 \times n = m n .$
$(n - 5) \times (m - 5) = 25$
$(n - 5) \times (m - 5) = 1 \times 25 o r 5 \times 5 o r 25 \times 1$
$s i n c e m \geq n; o n l y t w o c a s e s a r e p o s s i b l e$
$s o, t h e r e w i l l b e t w o p a i r s$

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How many pairs of positive integers (n.m) with n≤m satisfy the equation 15=1n+1m?

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How many pairs of positive integers $(n . m)$ with $n \leq m$ satisfy the equation $\frac{1}{5} = \frac{1}{n} + \frac{1}{m}$ ?