Question

Write the number 79 as the difference of the squares of two consecutive natural numbers and find the numbers.

Answer 1

Step-by-step explanation:

let two consecutive natural numbers be x and (x-1)

${x}^{2} - ( {x - 1) }^{2} = 79 \\ {x}^{2} - ( {x}^{2} + 1 - 2x) = 79 \\ \\ {x }^{2} - {x}^{2} - 1 + 2x = 79 \\ 2x = 79 + 1 \\ 2x = 80 \\ x = 40 \\ and \: (x - 1) = 40 - 1 \\ (x - 1) = 39$

therefore the two consecutive natural numbers are 40 and 39.