Question

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

Answer 1

$\Rightarrow$ Let smaller number be $x$ and larger number be $y$

According to the question,

$\Rightarrow$ $y^2-x^2=88$ ------ ( 1 )

$\Rightarrow$ $y=2x-5$ ----- ( 2 )

Substituting value of $y$ from equation $\left(2\right)$ in ( 1 )$,

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

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

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

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

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

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

$\Rightarrow$ $x-9=0$ and $3x+7=0$

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

Number cannot be negative.

$\therefore$ Smaller number $=9$

$\Rightarrow$ Larger number $=2x-5=2\times 9-5=18-5=13$

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