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help me with the following:
1.the sum of a whole number and its reciprocal is 10/3.what is the number?state a simpler way for solving this problem.
2.if x+1/x =√12,find x-1/x.
3.if 2x+3y=14 and 2x-3y=2,find xy.
4.if x-y=13 and xy=30,find x+y.

Answer :

Solution :
1) The sum of a whole number and its reciprocal is 10/3

ie  x + 
1/x = 10/3
 ( x² + 1 ) / x  = 10 /3
3x² + 3 = 10x
3x² -10x +3 = 0
3x² -9x -x +3 =0
3x(x - 3) -1(x - 3) =0
( 3x -1 ) ( x - 3 ) =0

hence x = 3 0r 1/3
since a whole number x = 3

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