Question

sum of the squares of two consecutive positive odd numbers is 74 .find those numbers by using quadratic equations

Answer 1

Let one be x
Therefore, another = (x+2)
According to question,

${x}^{2} + {(x + 2)}^{2} = 74 \\ {x }^{2} + x {}^{2} + 4 + 4x = 74 \\ 2 {x {}^{2} + 4x}^{} - 70 = 0 \\ {x}^{2} + 2x - 35 = 0 \\ {x}^{2} + 7x - 5x - 35 = 0 \\ x(x + 7) - 5(x + 7) = 0 \\ (x + 7)(x - 5) = 0 \\ x = ( - 7) \: \: \: or \: \: \: x = 5$

Given, Number is positive, Hence, x = 5

Hence the numbers are 5 and 7.