Question

the sum of the ages of father and his son is 42 years the product of their ages is 185 find the agents​

Answer 1

Answer:

Sum of ages of father and son = 42 years

Let father’s age be x years

Son’s age = (42 – x) years

∴  The age of his son is (42 – x) years.

As per the given condition,

x (42 – x) = 185

∴  42x – x2 = 185

∴  0 = x2 – 42x + 185

∴  x2 – 42x + 185 = 0

∴  x2 – 5x – 37x + 185 = 0

∴  x (x – 5) – 37 (x – 5) = 0

∴  (x – 5) (x – 37) = 0

∴  x – 5 = 0 or x – 37 = 0

∴  x = 5 or x = 37

∵ 5 years cannot be the age of Father.

∴ It is unacceptable,

∴  x = 37

And 42 – x = 42 – 37 = 5

The father’s age is 37 years and son’s age 5 years.

Answer 2

Father age → 37 years

Son Age → 5 years

Step-by-step explanation:

F + S = 42

F * S = 185

(42-S) * S = 185

42S - S² = 185

S² - 42S + 185 = 0

S² - 37S - 5S + 185 = 0

(S - 37) (S - 5) = 0

S = 37 or 5