Question

The sum of 2 consecutive natural number and square of first is 5329

Answer 1

Answer:

72, 73, 5184

Step-by-step explanation:

let the number be x

consecutive number will be x + 1

square of the first number be x^2

sum of the numbers is 5329

$x + x + 1 + {x}^{2} = 5329 \\ {x}^{2} + 2x + 1 = 5329 \\ {x}^{2} + 2x + 1 - 5329 = 0 \\ {x}^{2} + 2x - 5328 = 0 \\ {x}^{2} + 74x - 72x - 5328 = 0 \\ x(x + 74) - 72(x + 74) = 0 \\ (x + 74)(x - 72) = 0 \\ x + 74 = 0 \: \: \: \: x - 72 = 0 \\ x = - 74 \: \: \: \: \: \: \: \: \: \: x = 72$

we take the positive value of x = 72

the numbers are

x = 72

x + 1 = 72 + 1 = 73

x^2 = 72 × 72 = 5184

verification

72 + 73 + 5184 = 5329

hope you get your answer