Question

The sum of the squares of two consecutive odd numbers is $394$. The product of two numbers is:

Answer 1

$\Rightarrow$ Let two consecutive odd number be $x$ and $x+2$

According to the question,

$\Rightarrow$ $x^2+(x+2{)}^2=394$

$\Rightarrow$ $x^2+x^2+4x+4=394$

$\Rightarrow$ $2x^2+4x-390=0$

$\Rightarrow$ $x^2+2x-195=0$

$\Rightarrow$ $x^2+15x-13x-195=0$

$\Rightarrow$ $x(x+15)-13(x+15)=0$

$\Rightarrow$ $(x+15)(x-13)=0$

$\Rightarrow$ $x+15=0$ and $x-13=0$

$\Rightarrow$ $x=-15$ and $x=13$

$\therefore$ On number is $13$

$\Rightarrow$ Other number $=13+2=15$

$\Rightarrow$ Required product $=13\times 15=195$