Question

the sum of the square of two consecutive even number is 1252,the sum of the number is​

Answer 1

$\huge\text{\underline{Answer}}$

$\bold\red{24 and 28 }$

Let the two consecutive even number be x+2 , x+4 .

According to question,

$\bold{</strong> {(x + 2)}^{2} + {(x + 4)}^{2} = 1252<strong>}$

Solve for x

$\implies$ $\bold{( {x}^{2} + 4 + 4x) + ( {x}^{2} + 16 + 8x) = 1252}$

$\implies$ $\bold{ 2 {x}^{2} + 12x + 20 = 1252}$

$\implies$ $\bold{2 {x}^{2} + 12x - 1232 = 0}$

Solve as quadratic equation,

Dividing both side by 2 we get,

$\implies$ $\bold{ {x}^{2} + 6x - 616 = 0}$

$\implies$ $\bold{{x}^{2} + 28x - 22x - 616 = 0}$

$\implies$ $\bold{ x(x + 28) -22 (x + 28) = 0}$

$\implies$ $\bold{ (x - 22)(x + 28) = 0 }$

$\implies$ $\bold{x = 22 or x = -28 }$

Negative number is neglected

hence, the two even number are

24 and 28 .