The sum of two numbers “a” and “b” is 15, and the sum of their reciprocals . Find the numbers “a” and “b”.

Given: a + b = 15

To find: The value of a and b.

Method Used:

To solve the quadratic equation by factorisation method, follow the steps:

1) Multiply the coefficient of x² and constant term.

2) factorise the result obtained in step 1.

3) Now choose the pair of factors in such a way that after adding or subtracting(splitting) them

You get coefficient of x.

Explanation:

Numbers are ‘a’ and ‘b’

According to given conditions:

a + b = 15

⇒ b = 15 – a …. (1)

Also,

From (1),

⇒ 15 × 10 = 3(15a – a²)

⇒ 15 × 10 = 45a – 3a²

⇒ 3a² – 45a + 150 = 0

⇒ a² – 15a + 50 = 0

⇒ a² – 15a – 5a + 50 = 0

⇒ a (a – 10) – 5(a – 10) = 0

⇒ (a – 5) (a – 10) = 0

⇒ a = 5, 10

If a = 5, b = 15 – 5 = 10

If a = 10, b = 15 – 10 = 5

Hence, Numbers are 5,10 or 10, 5.