Question 53161
A NUMBER IS 21/10 MORE THAN ITS RECIPROCAL. FIND THE NUMBER.
:
21/10 can easily be handled as decimal; 2.1, so we can write it:
x = 1/x + 2.1
:
Mult equation by x to get rid of the denominator, you have:
x^2 = 1 + 2.1x
:
x^2 - 2.1x - 1 = 0 arranged as a quadratic equation
:
Solve for x your favorite method and you get
x = +2.5, x = -.4
:
if you prefer fractions:
x = 5/2, x = -4/10 
:
:
Check with x = 2.5
2.5 = (1/2.5) + 2.1
2.5 = .5 + 2.1
:
Check with x = -.4
-.4 = (1/-.4) + 2.1
-.4 = -2.5 + 2.1