You can put this solution on YOUR website! sol:
let the number be x
its reciprocal=1/x
7 times its reciprocal=7*1/x=7/x
according to the problem
sum of a number and 7 times its reciprocal=16/3
x+7/x=16/3
multiply both sides by x
x*x+7/x*x=16/3*x
x^2+7=16x/3
multiply both sides by 3
x^2*3+7*3=16x/3*3
3x^2+21=16x
transpose 16x from R.H.S to L.H.S
3x^2-16x+21=0
on multiplying two numbers we get 63 and adding or subtracting two numbers we get 16
those numbers are 7 and 9
7*9=63
and 7+9=16
3x^2-16x+21=0 can be written as
3x^2-9x-7x+21=0
3x(x-3)-7(x-3)=0
(3x-7)(x-3)=0
3x-7=0
3x=7
x=7/3
x-3=0
x=3
the number is 7/3 or 3
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