Question

If Aamir were younger by 7 years than what he really is, then the square of his age (in years) would have been 17 more than four times his actual age. What is his age now?​

Answer 1

Answer :-

The age of Aamir is 16 years.

Explanation :-

Let x = Aamir age

As per question given the following equation can be formed :

$⇒ {(x - 7)}^{2} =17+4x$

$⇒ {x}^{2} - 14x \: + 49 = 17 \: + 4x$

$⇒ {x}^{2} - 14x \: - 4x \: + 49 - 17 = 0$

$⇒ {x}^{2} - 18x \: + 32 = 0$

By splitting the middle term :-

$⇒ {x}^{2} - 16x \: - 2x \: + 32 = 0$

$⇒x \: (x \: - 16) \: - 2 \: (x \: - 16) = 0$

$⇒( \: x - 2)( x \: - 16) = 0$

So , x = 2 and x = 16

Since his age can't be 2 , So his age is 16 years

______________________________

Answer 2

Solution :-

Let us assume that, Aamir present age is x years .

So,

→ Aamir age 7 years ago = (x - 7) years .

A/q,

→ (x - 7)² = 4 * x + 17

using (a - b)² = a² + b² - 2ab in LHS,

→ x² + 49 - 14x = 4x + 17

→ x² - 14x - 4x + 49 - 17 = 0

→ x² - 18x + 32 = 0

→ x² - 16x - 2x + 32 = 0

→ x(x - 16) - 2(x - 16) = 0

→ (x - 16)(x - 2) = 0

→ x = 16 or 2 .

when x = 2

→ Aamir age 7 years ago = (2 - 7) = (-5) years .

• But age can't be in negative .

therefore , Aamir present age is 16 years .

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