Question

The sum of the ages of two friends is 20 years. Four years ago the product of their ages is 48 years. Is the situation possible ? If so determine their present ages.​

Answer 1

answer is given in picture

Answer 2

$\large{\red{\frak{question}}}$

The sum of the ages of two friends is 20 years. Four years ago the product of their ages is 48 years. Is the situation possible? If so determine their present ages.

$\large{\red{\frak{solution}}}$

let,

current age of two friends be,

'x' yrs and 'y' yrs

then,

$\boxed{\tt{x + y = 20}} - - eqn(1)$

and

four years ago their ages will be

x-4 and y -4

so,

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

xy -4x-4y+16=48

(putting x = 20-y)

(20-y)y-4(20-y) -4y+16=48

20y-y^2-80+4y-4y+16=48

we will get,

a quadratic polynomial

x^2-20x-112=0

that

will give us two distinct roots

which will not be whole numbers

while age should be always in whole numbers.

Hence, it is not possible.