Question

Represent the following situation in the form of quadratic equation and solve by quadratic formula. Rohan's mother is 26 years older than him. The product of there ages (in years) 3 years from now will be 360. Find the present age of Rohan.​

Answer 1

Answer:

let present age of rohan be x

rohan mother is X+26

after 3yrs from now rohan is X+3

rohan mother is X+29

Step-by-step explanation:

(X+3)(X+29)=360

Xsquare+32X+87=360

Xsquare+32X-273=0

x=7,-39

Answer 2

Answer:

The present age of Rohan is 7 years.

$\rule{100}2$

Solution :

Let the present age of Rohan be ' x '

So, present age of mother will be ' x + 26 '

After 3 years

• Rohan = ' x + 3 '
• Mother = ' x + 26 + 3 '  => x + 29

According to question :

( x + 3 ) × ( x + 29 ) = 360

⇒ x² + 29x + 3x + 87 = 360

⇒ x² + 32x + 87 = 360

⇒ x² + 32x = 360 - 87

⇒ x² + 32x = 273

⇒ x² + 32x - 273 = 0

Now factorise : x² + 32x - 273

⇒ x² + ( 39 - 7 )x - 273 = 0

⇒ x² + 39x -7x - 273 = 0

⇒ x ( x + 39 ) - 7 ( x + 39 ) = 0

⇒ ( x - 7 ) ( x + 39 ) =0

Now,

• x - 7 = 0 ; x = 7
• x + 39 = 0 ; x = - 39

But age cannot be in negative term. So, the age of Rohan is 7 years.

$\rule{200}2$