Question

Please , solve this fast .

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

$\mathfrak{\huge{Answer :}}$

4 and 32 years

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$\huge{\mathfrak{Brainly \: Solution :}}$

Let the son's age be = x
Father's age = 2x^2

$\bf 8 \: years \: later,$
Son age = x + 8

Father age = 2 x^2 +8

Since the difference between father and son age is 4.

According to question,

2x^2 + 8 - 3 ( x+8) = 4

2x^2 + 8 - 3x - 24 = 4

2x^2 -3x - 20 = 0

2x^2 + 8x - 5x - 20 = 0

2x ( x +4) -5 (x+4) = 0

(2x-5)(x+4) = 0

x+4 = 0

x = -4 ( age cannot be negative so we leave out the negative sign )

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$\large{\green{\sf{Son's \: age = 4}}}$

$\large{\green{\sf{Father \: age = 2{x}^{2} = 32}}}$

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Answer 2

▶ 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 :-

→ 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,

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



•°• Son's present age = 4 years, and

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



✔✔ Hence, it is solved ✅✅.



$\huge \blue{ \boxed{ \boxed{ \mathscr{THANKS}}}}$