Question

the sum of squares of three consecutive odd number is 1091.the greatest of these numbers is​

Answer 1

Answer:

Let the 3 consecutive odd integers be x, x + 2, x + 4.

Now,

${x}^{2} + {x + 2}^{2} + {x + 4}^{2} = 1091 \\ {x}^{2} + 4 + 4x + {x}^{2} + 16 + 8x = 1091 \\ 2 {x}^{2} + 12x + 20 = 1091 \\ 2 {x}^{2} + 12x - 1071 = 0$

Now, you can easily find the numbers by finding the solutions of the above quadratic equation.