Question

find two consecutive positive integers,sum of whose square is 365.​

Answer 1

Answer:

$x = - 14 \: and \: 13$✔✔

Step-by-step explanation:

LET FIRST POSSITIVE INTEGER BE = X

CONSECUTIVE INTEGER BE = X+1

ACCORDING TO QUESTIONS

$({x + 1})^{2} + {x}^{2} = 365 \\ {x}^{2} + 1 + 2x + {x}^{2} = 365 \\ 2 {x}^{2} + 2x + 1 - 365 = 0 \\ 2 {x}^{2} + 2x - 364 = 0 \\ 2 {x}^{2} - 26x + 28x - 364 = 0 \\2x(x - 13x) + 28(x - 13) = 0 \\ 2x + 28 = 0 \\ 2x = - 28 \\ x = \frac{ - 28}{2} \\ x = - 14 \\ x - 13 = 0 \\ x = 13$✔✔

Answer 2

$\huge{Refer To The Attachment}$