Question

the age of a man is twice the square of the age of his son. Eight years hence, the age of the man will be 4 years more than three times the age of his son. Find their present ages.

Answer 1

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Answer 2

▶ Answer :-

→ Son's present age = 4 years, and

man's present age = ( 2 × 4² ) years = 32 years .

▶ Step-by-step explanation :-

$\huge \pink{\mid \underline{ \overline{ \tt Solution :- }} \mid}$

→ Let the present age of the son be x years .

→ Then, the present age of the man is ( 2x² ) years .

→ Age of the son 8 years hence = ( x + 8 ) years .

→ Age of the man 8 years hence = ( 2x² + 8 ) years .

▶ Now,

$\begin{lgathered}\sf \because(2 {x}^{2} + 8) = 3(x + 8) + 4. \\ \\ \sf \implies2 {x}^{2} - 3x - 20 = 0. \\ \\ \sf \implies2 {x}^{2} - 8x + 5x - 20 = 0. \\ \\ \sf \implies2x(x - 4) + 5(x - 4) = 0. \\ \\ \sf \implies(x - 4)(2x + 5) = 0. \\ \\ \sf \implies x - 4 = 0. \: \: \green{or} \: \: 2x + 5 = 0. \\ \\ \sf \implies x = 4 \: \: \green{or} \: \: x = \frac{ - 5}{2} . \\ \\ \huge \boxed{ \boxed{\orange{ \sf \implies x = 4.}}} \\ \\ \bigg[ \tt \because age \: cannot \: be \: negative. \bigg]\end{lgathered}$

•°• Son's present age = 4 years, and

man's present age = ( 2 × 4² ) years = 32 years .

✔✔ Hence, it is solved ✅✅.