Question

sum of squares of two consecutive even numbers is 580.Find the numbers by writing a suitable quadratic equation

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

Answer 2

Answer:

x²+(x+2)²/580

x²+x²+4+4x=580

2x²+4x= 576

x²+2x=288

x²-16x+18x-288=0

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

(x+18)(x-16)

x=-18(or)16

If x is 16 the another number is 18

or

if x is -18 the another number is -16