The sum of the squares of two consecutive odd numbers i

The sum of the squares of two consecutive odd numbers i
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The sum of the squares of two consecutive odd numbers is 394. find the numbers.
 

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Right Answer is:

SOLUTION

Let one of the odd number be x.
Then the other odd number will be x+2.
According to question,
x squared plus left parenthesis x plus 2 right parenthesis squared equals 394 rightwards double arrow x squared plus x squared plus 4 x plus 4 equals 394 rightwards double arrow 2 x squared plus 4 x minus 390 equals 0 rightwards double arrow x squared plus 2 x minus 180 equals 0 rightwards double arrow x squared plus 15 x minus 13 x minus 180 equals 0 rightwards double arrow x left parenthesis x plus 15 right parenthesis minus 13 left parenthesis x plus 15 right parenthesis equals 0 rightwards double arrow left parenthesis x minus 13 right parenthesis left parenthesis x plus 15 right parenthesis equals 0 rightwards double arrow x equals 13 space o r space minus 15
Now if one number is 13 then the other number is 13+2=15. and if one number is -15 then the other number is -13.

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