Question

The sum of two numbers a and b is 15 and the sum of their reciprocal is 3/10 find the no.
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Answer 1

Numbers are a and b.

A.t.q,

a + b = 15

b = 15 - a ------(i)

Given that : 1/a + 1/b = 3/10

Putting value of b :

1/a + 1/15-a = 3/10

15 - a + a / 15a - a² = 3/10

15 = 45a - 3a² / 10

150 = 45a - 3a²

3a² - 45a + 150 = 0

3a² - 30a - 15a + 150 = 0

3a ( a - 10 ) - 15 ( a - 10 )

( 3a - 15 ) ( a - 10 )

3a = 15 or a = 10

a = 5

Case : a = 5

a + b = 15

5 + b = 15

b = 10

Numbers are 5 and 10.

Case : a = 10

a + b = 15

10 + b = 15

b = 15 - 10

b = 5

Numbers are 5 and 10.