Question

find two consecutive odd postive integers,sum of whose squares is 290​

Answer 1

Step-by-step explanation:

Let the smaller of the two consecutive odd positive integers be x. Then the second integer will be x + 2. According to the question x2 + x + 22 = 290i.e. x2 + x2 + 4x + 4 = 290i.e. 2x2 + 4x – 286 = 0i.e. x2 + 2x – 143 = 0which is a quadratic equation in x.Using the quadratic formula we getBut x is given to be an odd positive integer. Therefore x≠ – 13 x = 11.Thus the two consecutive odd integers are 11 and 13.Check : 112 + 132 = 121 + 169 = 290.