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The sum of two numbers is 9 and the sum of their reciprocals is 1÷2. Find the numbers

Posted by Aaron Pulikkottil 6 years, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 3 months ago

Let one number be x.

Then, another number = (9 - x) [{tex}\because{/tex} sum of two numbers = 9]

According to the question,
{tex}\begin{array}{l}\frac1x+\;\frac1{9-x}=\;\frac12\\\frac{9\;-x+x}{x(9-x)}\;=\frac12\end{array}{/tex}

⇒ 18 = 9x - x²

{tex}\Rightarrow {x^2} - 9x + 18 = 0 {/tex}

{tex}\Rightarrow {x^2} - 6x - 3x + 18 = 0{/tex}
{tex}\Rightarrow x=3,x=6{/tex}

When, x = 3, then 9 - x = 9 - 3 = 6

When, x = 6, then 9 - x = 9 - 6 = 3

Hence, the numbers are 3 and 6.

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