Question

The sum of two nos. a and b is 15 and the sum of their reciprocals 1/a and 1/b is 3/10. Find the numbers a and b.​

Answer 1

Answer

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.

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Answer 2

Answer:

a = 5 and b = 10

Step-by-step explanation:

a+b=15 ..................(i)

1/a+1/b= 3/10

b+a/ab= 3/10

15/ab = 3/10   (∵ a+b= 15)

50=ab

a= 50/b............(ii)

Putting value of a in eq.1

50/b+b= 15

50+b²= 15b

b²-15b+50=0

b²-10b-5b+50 = 0

b(b-10)+5(b-10) = 0

∴ b=10 and, b= -5

value of cannot be negative

∴b = 10

using eq. 2 we get,

a=5

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