The sum of squares of two consecutive natural numbers is 244; find the numbers. Solve the word problem
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Let, the the number be x
∴ it's consecutive number will be x +1
∴ According to the given condition
x² + (x+2)² = 244
∴ x² + x² + 4x + 4 = 244
∴ 2x² + 4x +4 = 244
∴ 2x² + 4x +4 - 244 = 0
∴ 2x² + 4x - 240 = 0
∴ 2x² + 24x - 20x -240 = 0
∴ 2x (x + 12 ) - 20 (x + 12)
∴ (x + 12) (2x - 20) = 0
∴ x + 12 = 0 Or 2x - 20 = 0
∴ x = -12 Or x = 20/2
x = 10
∴ it's consecutive number will be x +1
∴ According to the given condition
x² + (x+2)² = 244
∴ x² + x² + 4x + 4 = 244
∴ 2x² + 4x +4 = 244
∴ 2x² + 4x +4 - 244 = 0
∴ 2x² + 4x - 240 = 0
∴ 2x² + 24x - 20x -240 = 0
∴ 2x (x + 12 ) - 20 (x + 12)
∴ (x + 12) (2x - 20) = 0
∴ x + 12 = 0 Or 2x - 20 = 0
∴ x = -12 Or x = 20/2
x = 10
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