Quadratic equations please help
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12. Find two consecutive odd positive integers, sum of whose squares is 290.

Dear Student,

(12).
 

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 are positive integers)

⇒x + 2 = 11+2=13

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

Kindly ask the remaining queries in different threads.

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