Question

Sum of 3 numbers which are in AP is 27 and if the sum of squares of this 3 numbers is 293 find the numbers

Answer 1

Answer:

4, 9, 14

Step-by-step explanation:

let first term be a

and common difference = d

given,

a + (a+d) + (a+2d) = 27

            => 3a + 3d = 27

            => a+d = 9 or a = 9-d  (x)

a² + (a+d)² + (a+2d)² = 293

           => a² +  (9)²  + (9+d)² = 293

          => a² + 81 + 81 + d² + 18d = 293

         => a² + d² + 18d = 131

substituting value of a from (x) in above equation

        => (9 - d)² + d² + 18d = 131

       => 81 + d² + d² -18d + 18d = 131

       => 2d² = 50 => d² = 25

      => d = 5

 => a = 9-5 = 4

Hence, 3 numbers are a, a+d, a+2d => 4, 9, 14