Question

The age of Kathik in 11 years will be a perfect square. If his present age is also a perfect square, what
his present ages​

Answer 1

Answer:

25

Step-by-step explanation:

25+11=36(perfect square)

Answer 2

Answer:25 years

Step-by-step explanation:

Given that the age of karthik after 11 years will be a perfect square and also his present age is a perfect square.

So assuming;-

The present age to be x years,

And and the age after 11 years be y years,

Now, as the equation relating x and y is:-

y = x+11(As the age of the person after 11 years is y).

As both are perfect squares we assume:-

x=$p^{2}$ and y=$q^{2}$ where both are p,q are integers.

And now by equation relating x and y:-

$q^{2}$=$p^{2}$+11,

So,

$q^{2}$-$p^{2}$=11,

The difference of squares of two integers is 11.

We say that the integers are:-

q=6 and p=5(By clear inspection of difference of squares)

As by expanding the LHS of the equation:-

(q+p)(q-p)=11,

here both are naturals p+q and p-q so they are 11 and 1 as 11 is a prime number and it can be expressed as 11×1. only and obviously p+q is greater then q-p.

So, solving this gives:-

p+q=11 and q-p=1 adding them gives,

2q=12 so q=6 and putting q in p+q=11 gives

p=5.

And the present age in terms of p is $p^{2}$

Answer is 5×5=25years Answer:-25years.

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