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# The Sum of Two Numbers is 9. the Sum of Their Reciprocals is 1/2. Find the Numbers. - Mathematics

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#### Question

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

#### Solution

Let one numbers be then other (9 - x).

Then according to question

1/x + 1(9-x)=1/2

rArr((9-x)+x)/(x(9-x))=1/2

rArr9/(x(9-x))=1/2

By cross multiplication

⇒ 18 = x(9 - x)

⇒ x2 - 9x + 18 = 0

⇒ x2 - 6x - 3x + 18 = 0

⇒ x(x - 6) - 3(x - 6) = 0

⇒ (x - 6)(x - 3) = 0

⇒ x - 6 = 0

⇒ x = 6

Or

⇒ x - 3 = 0

⇒ x = 3

Since, x being a number,

Therefore,

When x = 6 then

(9 - x) = (9 - 6) = 3

When x = 3 then

(9 - x) = (9 - 3) = 6

Thus, two consecutive number be either 3, 6 or 6, 3.

Is there an error in this question or solution?
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#### APPEARS IN

RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.7 | Q: 31 | Page no. 52
RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.7 | Q: 31 | Page no. 52
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Solution The Sum of Two Numbers is 9. the Sum of Their Reciprocals is 1/2. Find the Numbers. Concept: Solutions of Quadratic Equations by Factorization.
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