Question

The sum of the ages of two friends is 20 years.Four yaer ago,the product of their ages in year was 48.

Answer 1

Hey

Here is your answer,

Let the age of one friend be x years.

Age of the other friend will be (20 − x) years.

4 years ago, age of 1st friend = (x − 4) years

And, age of 2nd friend = (20 − x − 4)

= (16 − x) years

Given that,

(x − 4) (16 − x) = 48

16x − 64 − x2 + 4x = 48

− x2 + 20x − 112 = 0

x2 − 20x + 112 = 0

Comparing this equation with ax2 + bx + c = 0, we obtain

a = 1, b = −20, c = 112

Discriminant = b2 − 4ac = (− 20)2 − 4 (1) (112)

= 400 − 448 = −48

As b2 − 4ac < 0,

Therefore, no real root is possible for this equation and hence, this situation is not possible.


Hope it helps you!

Answer 2

Answer: Given,

Sum of age of friend=20 years

Product of age of friend 4 years ago=48 years

Step-by-step explanation:Now,

Let the age of first friend be x and second be y.

Now,

Age of first friend 4 years ago= x-4

Age of second friend 4 years ago= y-4

Now,

x+y =20

→ y=20-x

(x-4)(y-4) =48

→(x-4)(20-x-4)=48

→(x-4)(-x+16)= 48

→-$x^{2}$ +16x + 4x - 64=48

→$x^{2}$+20x - 112 =0

So,

If we want to find their ages we will use the discriminate if the discriminate is a real number than only it is possible to find the the age , if it is a imaginary number we can't find the age.

Now, compare the equation with a$x^{2}$+bx+c=0

So, we will have

a=1 , b=20 , c=-112

Now,

Discriminate = $b^{2}$- 4ac

                      =$(20)^{2}$- 4(1)(-112)

                      =400-448

                      =-48

Since the discriminate is a imaginary number we can't find their ages.