Question

The sum of the square of three consecutive natural numbers is 302.What is the middle number

Answer 1

let the numbers be x, x+1, x+2

x² + (x+1)²+ (x+2)² = 302

x² + x² + 2x + 1 + x² +4x + 4= 302

3x² + 6x + 5 = 302

3x² +6x + 5 - 302 = 0

3x² + 6x - 297 = 0

3x² + 33x - 27x - 297 = 0

3x(x + 11) - 27(x + 11) = 0

(3x  - 27)(x + 11)

x = -11 (rejected becoz natural no. can't be zero)

x= 27/3 = 9

middle number = x + 1 i.e 9 + 1 = 10

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