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Question Number 211595 by BaliramKumar last updated on 14/Sep/24

Answered by mr W last updated on 14/Sep/24

m^2 −n^2 =199  (m−n)(m+n)=1×199  m−n=1  m+n=199  ⇒m=((1+199)/2)=100, n=((199−1)/2)=99  ⇒mn=9900

$${m}^{\mathrm{2}} −{n}^{\mathrm{2}} =\mathrm{199} \\ $$$$\left({m}−{n}\right)\left({m}+{n}\right)=\mathrm{1}×\mathrm{199} \\ $$$${m}−{n}=\mathrm{1} \\ $$$${m}+{n}=\mathrm{199} \\ $$$$\Rightarrow{m}=\frac{\mathrm{1}+\mathrm{199}}{\mathrm{2}}=\mathrm{100},\:{n}=\frac{\mathrm{199}−\mathrm{1}}{\mathrm{2}}=\mathrm{99} \\ $$$$\Rightarrow{mn}=\mathrm{9900} \\ $$

Commented by BaliramKumar last updated on 14/Sep/24

thanks

$${thanks} \\ $$

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