Question

In the following question, two statements (i) and (ii) are given. Choose the valid statement.

1. The roots of equation 6x² − 5x + 1= 0 are `1/2 and 1/3.`
2. The sum of two numbers is 7 and the sum of their reciprocals is `7/12`. Then smaller number is 3.

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Both (i) and (ii)

Explanation:

Statement (i):

Given equation: 6x² − 5x + 1 = 0

6x² − 5x + 1 = (3x − 1) (2x − 1) = 0

`x = 1/3, 1/2`

Statement (i) is true.

Statement (ii):

Let the two numbers be aaa and b.

Given:

a + b = 7

`1/a + 1/b = 7/12`

`(a+b)/(ab) = 7/12`

`=> 7/(ab) = 7/12`

⇒ ab = 12

So the numbers satisfy:

x² − 7x + 12 = 0

⇒ (x − 3) (x − 4) = 0

Numbers are 3 and 4.

Smaller number is 3.

Statement (ii) is true.