Question

the sum of the square of three consecutive odd numbers is 2531 find the numbers

Answer 1

take no. be x,x+2,x+4

now according to question..

${x}^{2} + ({x + 2})^{2} + ({x + 4})^{2} = 2531$


now make quadratic equation and solve it

Answer 2

Let the 1st no is n, second is (n+2) and the third is (n+4).
so, n^2+(n+2)^2+(n+4)^2 =2531
n^2 + n^2 + 4n + 4 + n^2 + 8n + 16 = 2531
3n^2 + 12n -2511=0
n^2 + 4n -837 =0
n^2 + (31-27)*n -27*31=0
n^2 + 31n - 27n - 27*31=0
n(n+31) - 27(n+31)=0
(n+31)(n-27)=0
since n can not be (-31) because it is negative.
so n=27
and the other odd numbers are (n+2=) 29 and (n+4=) 31