Question

Quadratic Equation

The sum of the ages of two friends is 13 years and the product
of their ages is 42. Find their ages.​

Answer 1

Explanation:

The sum of ages of two friends is 13 years.

The product of their ages is 42.

Let the age of 1st friend and 2nd friend is x, y respectively.

1 st condition= The sum of ages of two friends is 13 yrs.

i.e x+y = 13........ (I)

2nd condition= The product of their ages is 42.

i.e X*y = 42........(ii)

From equation (I)

X+y = 13

or, X = 13-y........ (iii)

Putting the equation (iii) in equation (ii).

X*y= 42

(13-y) * y = 42

13y - y^2 = 42

`{y}^(2) - 13y + 42 = 0`

`{y}^(2) - (7 + 6)y + 42= 0`

`{y}^(2) - 7y - 6y + 42 = 0`

`y(y - 7) - 6(y - 7) = 0`

`(y - 6) (y - 7) = 0`

Either; y-6 = 0

y = 6

Or;

y-7=0

y = 7

Keeping the value of y as "7" in equation (ii)

x*y = 42

7x = 42

X = 42/7

Therefore, the value of X is 6.

Therefore, either 1st friend is 6 years and 2nd is 7 years.

Hope it helps...