Question

A year ago, the father was 8 times as old as his son. Now his age is the square of his son's age. Find his present age.

Answer 1

Answer:

Step-by-step explanation:

Now his age is the square of his son's age. Find their present ages. ∴ x = 1 is rejected. and present age of father = 49 years.

Answer 2

GivEn:-

• A year ago, the father was 8 times as old as his son.
• Now his age is the square of his son's age.

To find:-

• Present age of son and his father.

SoluTion:-

☯ Lets present age of the son be x years.

$\therefore$ Present age of father = x²

One year ago,

☯ Age of son = (x - 1) years

☯ And age of father = (x² - 1) years

$\dag\;{\underline{\underline{\bf{\pink{According\;to\;QuesTion:-}}}}}$

$\implies\sf x^2 - 1 = 8(x - 1)$

$\implies\sf x^2 - 1 = 8x - 8$

$\implies\sf x^2 - 8x = - 8 + 1$

$\implies\sf x^2 - 8x = - 7$

$\implies\sf x^2 - 8x = - 7$

$\implies\sf x^2 - 8x - 7 = 0$

$\small\sf\;\;\star\; \underline{Now,\; splitting \;the \;Middle \;term:-}$

$\implies\sf (x - 1)(x - 7) = 0$

$\;\;\;\small\sf\dag\; \underline{Here,\;both\;(x - 1)\;and\;(x + 7)\;equals\;to\;0.}$

$\implies\sf (x - 1) = 0\;;\;(x - 7) = 0$

$\implies\sf x = 1\;;\;x = 7$

$\implies\bf x = 1, 7$

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Therefore,

• x = 1, 7

• x² = (1)² , (7)² = 1,49

$\dag$ Hence, Present age of son (x) is 7 and Present age of his father (x²) is 49.

$\because$ Present Age of father = 1, is not possible

and age of father and son can't be same.

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