Question

The sum of the squares of two consecutive even numbers is $340$. The product of the numbers is:

Answer 1

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

According to the question,

$\Rightarrow$ $x^2+(x+2{)}^2=340$

$\Rightarrow$ $x^2+x^2+4x+4=340$

$\Rightarrow$ $2x^2+4x+4=340$

$\Rightarrow$ $2x^2+4x+4-340=0$

$\Rightarrow$ $2x^2+4x-336=0$

$\Rightarrow$ $x^2+2x-168=0$

$\Rightarrow$ $x^2+14x-12x-168=0$

$\Rightarrow$ $x(x+14)-12(x+14)=0$

$\Rightarrow$ $(x+14)(x-12)=0$

$\Rightarrow$ $x+14=0$ and $x-12=0$

$\Rightarrow$ $x=-14$ and $x=12$

$\therefore$ One number is $12$

$\Rightarrow$ Other number $=12+2=14$

$\Rightarrow$ Required product $=12\times 14=168$