Answer:
x=3 or x= 1/3
Step-by-step explanation:
Let the number = x
The reciprocal of the number = 1/x
According to the given statement:
x+1/x=10/3
x²+1/x=10/3
3(x²+1)=10x
3x²+3=10x
Move 10x to the L.H.S
3x²-10x+3=0
Break the middle term:
3x²-9x-x+3=0
3x(x-3)-1(x-3)=0
(x-3)(3x-1)=0
x-3=0 , 3x-1=0
x=0+3 , 3x=0+1
x=3 , 3x=1
x=3 ,x = 1/3
So x=3 or x= 1/3 ....
