Question

Find two consecutive of odd integers sum of all squares is 290

Answer 1

Answer:

Step-by-step explanation:

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here it is ;

Let one of the odd positive integer be x  

then the other odd positive integer is x+2

their sum of squares = x² +(x+2)²

                              = x² + x² + 4x +4

                              = 2x² + 4x + 4

Given that their sum of squares = 290

⇒ 2x² +4x + 4 = 290

⇒ 2x² +4x = 290-4 = 286

⇒ 2x² + 4x -286 = 0  

⇒ 2(x² + 2x - 143) = 0  

⇒ x² + 2x - 143 = 0

⇒ x² + 13x - 11x -143 = 0  

⇒ x(x+13) - 11(x+13) = 0  

⇒ (x-11) = 0 , (x+13) = 0

Therfore , x = 11 or -13

We always take positive value of x  

So , x = 11 and (x+2) = 11 + 2 = 13  

Therefore , the odd positive integers are 11 and 13 .