Question

the two consective positive even number whose sum of their square is 580

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

4x

2

+4x

2

+4+8x=580

8X

2

+8x+4−580=0

8x

2

+8x−576=0

x

2

+x−72=0⇒ Required quadratic equation.

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×−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.

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