Question

the sum of the ages of two friends is 20 years . four years ago the product of their ages in years was 48​

Answer 1

Correct Question :

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

Answer :

↪Let the present age of of one friend be ' x '

↪Age of other friend will be ( 20 - x )

● 4 years ago ,

↪One friend's age = ( x - 4 ) years

↪Another friend's age = ( ( 20 - 4 ) - x ) = ( 16 - x )

According to the condition :

⟹ ( x - 4 ) ( 16 - x ) = 48

⟹ $16x\:-\:x^2\:-\:64\:+\:4x\:=\:48$

⟹ $x^2\:-\:20x\:+\:112\:=\:0$

$\boxed{This\:is\:of\:the\:form\:\:ax^2\:+\:bx\:+\:c\:=\:0}$

Final Equations will be :

• a = 1
• b = -20
• c = 112

⟶ Discriminant ( D ) = $b^2\:-\:4ac$

➳ $( -20 )^2 - 4 × 1 × 112$

➳ 400 - 448 = -48 < 0

To find :

● No real Root Exist

● The given situation is not possible

So, It's Done !!