Answer:
11 and 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
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Answers & Comments
Answer:
11 and 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