Question

The difference of squares of two number is $88.$ If the larger number is $5$ less than twice the smaller number, then find the two numbers.

Answer 1

Let the smaller numbers be $x$

Then according to the question, we have

The larger number be $=2x-5$, then

Given: Difference of squares is $88$

(Larger no.)${}^2-$ (Smaller no.)${}^2=88$

$\therefore (2x-5{)}^2-x^2=88$

$\Rightarrow 4x^2-20x+25-x^2-88=0$

$\Rightarrow 3x^2-20x-63=0$

$\Rightarrow 3x^2-27x+7x-63=0$

$\Rightarrow 3x(x-9)+7(x-9)=0$

$\Rightarrow (x-9)(3x+7)=0$

$\Rightarrow (x-9)=0or,(3x+7)=0$

$\Rightarrow x=9or,x=-\frac{7}{3}$

Since, $x$ being a positive integer so, $x$ cannot be negative,

Therefore, $x=9$, then larger number will be

$2x-5=2\times 9-5=18-5=13$

Product of two numbers $=9\times 13=117$

Hence, the product is $117$