Q) Find two consecutive odd positive integers, the sum of whose squares is by using the quadratic formula.

Ans: 

Let’s consider the 1st odd positive integer be X
Then the next consecutive odd positive integers will be X + 2

Now it is given, that the sum of the squares of these two numbers is 290
∴ X² + (X + 2)² = 290
∴ X² + (X² + 4 X + 4) = 290
∴ 2 X² + 4 X + 4 = 290
∴ 2 X² + 4 X – 286 = 0
∴ X² + 2 X – 143 = 0
∴ (X + 13) (X – 11) = 0
∴ X = – 13 and X = 11

Since the integer required to be positive,
therefore X -13 and X = 11
And the next integer is X + 2 = 11 + 2 = 13

Hence, the two consecutive positive odd integers are 11 & 13.

Please do press “Heart” button if you liked the solution.