Three consecutive natural numbers are such that the square of the midd

1.	Three consecutive natural numbers are such that the square of the middlenumber exceeds the difference of the squaren of thg other two hy 60. Find thenumbersx"
Answer» Since the middle number of the three consecutive numbers is x, the other two numbers are x -1 and x +1. According to the given condition, we have x² = [(x +1)² -(x -1)²] +60 x² = (x² +2x +1) -(x² -2x +1) +60 = 4x +60 x² -4x -60 = 0 => (x -10)(x +6) = 0 x = 10 or -6 Since x is a natural number, we get x = 10 Hence the three numbers are 9, 10, 11

Three consecutive natural numbers are such that the square of the middlenumber exceeds the difference of the squaren of thg other two hy 60. Find thenumbersx"

Answer»

Since the middle number of the three consecutive numbers is x, the other two numbers are x -1 and x +1.

According to the given condition, we have

x² = [(x +1)² -(x -1)²] +60

x² = (x² +2x +1) -(x² -2x +1) +60 = 4x +60

x² -4x -60 = 0 => (x -10)(x +6) = 0

x = 10 or -6

Since x is a natural number, we get x = 10

Hence the three numbers are 9, 10, 11