1.

The sum of the squaresof two consecutive odd numbers is 394. Find the numbers.

Answer» Let the requaired consecutive odd numbers be x and `(x+2).` Then,
`x^(2)+(x+2)^(2)=394`
`implies" "2x^(2)+4x-390=0impliesx^(2)+2x-195=0`
`implies" "x^(2)+15x-13x-195=0`
`implies" "x(x+15)-13(x+15)=0`
`implies" "x+15=0" or "x-13=0`
`implies" "x=-15" or "x=13`
`implies" "x=13." "["rejecting "x=-15]`
Hence, the required numbers are 13 and 15.


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