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Question

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

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Solution

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+4580=0
8x2+8x576=0
x2+x72=0 (Taking 8 common)
x2+9x8x72=0
(x+9)(x8)=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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