Question:
2)Find two consecutive odd positive integers, Sum of whose squares is 290.
Answer:
Let the two consecutive odd numbers are a and a + 2
Given, sum of square of two consecutive odd numbers is 290
=> a2 + (a + 2)2 = 290
=> a2 + a2 + 4a + 4 = 290
=> 2a2 + 4a + 4 = 290
=> 2a2 + 4a + 4 - 290 = 0
=> 2a2 + 4a - 286 = 0
=> 2(a2 + 2a - 143) = 0
=> a2 + 2a - 143 = 0
=> a2 + 13a - 11a - 143 = 0
=> a(a + 13) - 11(a + 13) = 0
=> (a + 13)*(a - 11) = 0
=> a = 11, -13
Since number is positive,
So, a = 11
Now, a + 2 = 11 + 2 = 13
So, the numbers are 11 and 13
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