## Answer :

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

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.

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