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The difference of 2 numbers is 4 and difference of their reciprocals is 4/2. Find the numbers

Posted by Tanisha Shah 5 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Let the two numbers be x and x – 4.
Given that the difference of two numbers is 4.
By the given hypothesis, we have {tex}\frac{1}{x-4}-\frac{1}{x}=\frac{4}{21}{/tex}
{tex}\Rightarrow \frac{x-x+4}{x(x-4)}=\frac{4}{21}{/tex}
{tex}\Rightarrow 84 = 4x(x-4){/tex}
{tex}\Rightarrow x^2 - 4x -21=0{/tex}
{tex}\Rightarrow x^2 -7x+3x-21{/tex}
{tex}\Rightarrow (x-7)(x+3) = 0{/tex}
{tex}\Rightarrow x=7 \ or\ x=-3{/tex}
If x = 7, then {tex}x-4=7-4=3{/tex}
If x = -3, then {tex}x-4=-3-4=-7{/tex}
Hence, required numbers are 3,7 and -3,-7

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CBSE > Class 10 > Mathematics