Question

find the sum of 2 consecutive odd positive integers whose sum of squares is 290....
plzz respond with explaination it's urgent ​

Answer 1

Answer:

the number is 11 and the consecutive odd number is 13

Step-by-step explanation:

Let the two consecutive odd positive integers be x and x + 2

Now it is given that the sum of the squares is 290.

x² + ( x + 2 )² = 290

x² + x² + 4x + 4 = 290

 2x² + 4x + 4 - 290 = 0

2x² + 4x - 286 = 0

Dividing by 2 we get,  

x² + 2x - 143 = 0

x² + 13x - 11x - 143 = 0

x ( x + 13 ) -11 ( x + 13 ) = 0

 ( x - 11 ) ( x + 13 ) = 0

x = -13, 11

In the question we are given with positive integers.

Hence the number is 11 and the consecutive odd number is 13.

Hence these are the required numbers.