Question

Sum of squares of 2 consecutive even numbers is 580

Answer 1

Let the two consecutive even numbers be x and x+2

given that the sum of their squares = 580

⇒ x² + (x+2)² = 580

x² + x² + 4 + 4x = 580

2x² + 4x - 576 = 0

x² + 2x - 288 = 0

x² + 18x - 16x - 288 = 0

x(x+18) - 16 (x+18) = 0

(x+18) (x-16) = 0

x = - 18 or x = 16

If x = -18

then the two consecutive even numbers are -18, -20

If x = 16

then the two consecutive even numbers are 16 and 18

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hope it will help

Answer 2

Hi..

let two no. be x and (x+2)

given:-

${x}^{2} + {(x + 2)}^{2} = 580$

${x}^{2} + {x}^{2} + 4+ 4x = 580$

$2 {x}^{2} + 4x = 580 - 4$

$2 {x}^{2} + 4x - 576 = 0$

NOW YOU CAN APPLY QUADRATIC FORMULA AND FIND ITS ZEROES....

${b}^{2} - 4ac.......star$

${4}^{2} + 4 \times 2 \times 576$

$16+ 4608$

$4624$

$x = \frac{ - b( + - ) \sqrt{star} }{2a}$

$x = \frac{ - 4( + - ) \sqrt{424} }{2 \times 2}$

$x = \frac{ - 4 +68 }{4} ... \frac{ - 4 - 68}{4}$

$x = \frac{64}{4} \: \: or \: x = \frac{-72}{4}$

so, x = 16 or x= -18

if x be positive,
then no. would be 16 and 18

if x be negative
then no. would be -18 and -16

#THANKS