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Two consecutive even positive integers, what is the sum of the squares of which is 1060?

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Cambridge-Trained Ex-IITian Math Faculty for AS/A Level Math; IB Math; ISc Math and HSc Math

Let the two consecutive EVEN integers be 2x and 2x+2 Now, (2x)2 + (2x+2)2 =1060. Therefore, 4x2 + 4x2 + 8x+4 =1060.... because 8x2 + 8x+4 =1060 Dividing by 4, we get 2x2 + 2x+1 =265 or 2x2 + 2x-264 = 0 .......(1) Now, we find factors of 2 x (-264) = -528 which add upto +2 Let’s see: (+ 24) x (-22)...
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Let the two consecutive EVEN integers be 2x and 2x+2 Now, (2x)2 + (2x+2)2 =1060. Therefore, 4x2 + 4x2 + 8x+4 =1060.... because [ (a+b)2 = a2+2ab+b2] 8x2 + 8x+4 =1060 Dividing by 4, we get 2x2 + 2x+1 =265 or 2x2 + 2x-264 = 0 .......(1) Now, we find factors of 2 x (-264) = -528 which add upto +2 Let’s see: (+ 24) x (-22) = -528 Therefore, we write (1) as 2x2 + 24x-22x -264 = 0 2x(x+12)-22x(x+12)=0 (2x-22x)(x+12) =0 Therefore , 2x-22x = 0 OR x + 12 = 0 2x =22x OR x = -12 (we reject x = -12 because we know that the integers are positive) Therefore, x =11 Therefore, the integers are 2x = 22 and 2x+2 = 24. Therefore, the consecutive integers are 22 and 24. read less
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