Question

find two consecutive odd positive integers sum of whose squares is 290.

Answer 1

Dear student

Let the two consecutive odd number be x and x + 2.

Given: Sum of the squares of two consecutive odd positive integers is 290.

According to question,

⇒(x)²+(x + 2)²= 290

⇒x² + x² + 4x + 4 = 290

⇒2x²+ 4x + 4 = 290

⇒2x²+ 4x = 290 - 4

⇒2x² + 4x = 286

⇒x²+ 2x = 143

⇒x² + 2x - 143 = 0

⇒x² + 13x - 11x -143=0

⇒x(x + 13) -11(x + 13 )=0

⇒x = 11 (since they r positive integers)

⇒x + 2 = 11+2=13

Thus, the two consecutive odd positive integers are 11 and 13.


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