Question

find two consecutive positive even numbers if SUM of their square is 20​

Answer 1

Answer

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

Given that the sum of squares numbers is 580.

Therefore,

(2x)2+(2x+2)2=580

4x2+4x2+4+8x=580

8X2+8x+4−580=0

8x2+8x−576=0

x2+x−72=0⇒ Required quadratic equation.

x2+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×−9=−18

2x++2=2×−9+2=−16

Case II:- x=8

Therefore, the required numbers are-

2x=2×8=16

2x+2=2×8+2=18

Hence the required numbers are −18 and −16 or 16 and 18.