Question

-ii) the sum of the squares of two consecutive even natural number is 244. find the number
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Answer 1

Answer: 10 and 12

explanation: let the even consecutive no. be x and x+2

according to the question

(x)^2 + (x+2)^2 = 244

x^2 + x^2+ 4+ 4x = 244

2x^2 + 4x= 244-4

2x^2 + 4x= 240

2x^2 + 4x- 240 = 0

2(x^2 + 2x - 120 ) = 0

x^2 + 12x - 10x - 120 = 0

(x^2 + 12x) + (- 10x - 120 ) = 0

x(x+12) -10(x+12) = 0

(x-10) (x+12) = 0

x= 10, -12

Thus, the numbers are 10 and 12