Question

Sum of squares of two consecutive even number is $580$.Find the number by writing a suitable Quadratic equation.

Answer 1

Let $2x$ and $2x+2$ be the required even numbers.

Given that the sum of squares numbers is $580$.

Therefore,

${\left(2x\right)}^2+{(2x+2)}^2=580$

$4x^2+4x^2+4+8x=580$

$8x^2+8x+4-580=0$

$8x^2+8x-576=0$

$x^2+x-72=0$ (Taking 8 common)

$x^2+9x-8x-72=0$

$(x+9)(x-8)=0$

$x=-9$ or $x=8$

Case I:- $x=-9$

Therefore, the required numbers are-

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

$2x++2=2\times -9+2=-16$

Case II:- $x=8$

Therefore, the required numbers are-

$2x=2\times 8=16$

$2x+2=2\times 8+2=18$

Hence the required numbers are $-18$ and $-16$ or $16$ and $18$.