The sum of half a number and its reciprocal is the same as 51 divided by the number. How do you find the number?

Answer 1

Kennedy Adams

Write an equation to represent the situation

#x/2# + #1/x# = #51/x#

Place on a common denominator:

#(x(x))/(2(x))# + #(1(2))/(2(x))# = #(51(2))/(2(x))#

Now you can eliminate the denominators and solve the resulting quadratic equation.

#x^2# + 2 = 102

#x^2# - 100 = 0

Solve by factoring as a difference of squares.

(x + 10)(x - 10) = 0

x = -10 and 10

The numbers are -10 and 10.

Exercises:

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Trending questions

Not the question you need?

HIX Tutor

Solve ANY homework problem with a smart AI

98% accuracy study help
Covers math, physics, chemistry, biology, and more
Step-by-step, in-depth guides
Readily available 24/7