The sum of two numbers is 9- If the sum of their reciprocals is 1-2- find the numbers-

Let the first number = x Therefore the second number = 9 x According to question; Therefore if the first number is 3 then the second number is 6 and if the fir ...

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Standard X

Mathematics

Solving a Quadratic Equation by Factorization Method

The sum of tw...

Question

The sum of two numbers is 9. If the sum of their reciprocals is $\frac{1}{2}$ , find the numbers.

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Solution

Let the first number = x
Therefore the second number = 9-x
According to question;
$1 over x plus fraction numerator 1 over denominator 9 minus x end fraction equals 1 half rightwards double arrow fraction numerator 9 minus x plus x over denominator x left parenthesis 9 minus x right parenthesis end fraction equals 1 half rightwards double arrow 18 equals 9 x minus x squared rightwards double arrow x squared minus 9 x plus 18 equals 0 rightwards double arrow x squared minus 6 x minus 3 x plus 18 equals 0 rightwards double arrow x left parenthesis x minus 6 right parenthesis minus 3 left parenthesis x minus 6 right parenthesis equals 0 rightwards double arrow left parenthesis x minus 3 right parenthesis left parenthesis x minus 6 right parenthesis equals 0 rightwards double arrow x equals 3 space o r space 6$
Therefore if the first number is 3 then the second number is 6 and if the first number is 6 then the second number is 3.

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The sum of two numbers is 9. If the sum of their reciprocals is 12, find the numbers.

Let the first number = x Therefore the second number = 9-x According to question; Therefore if the first number is 3 then the second number is 6 and if the first number is 6 then the second number is 3.

The sum of two numbers is 9. If the sum of their reciprocals is $\frac{1}{2}$ , find the numbers.