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

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Answer 1 · 2016-01-25T20:26:08

Write an equation to represent the situation

$\frac{x}{2}$ $x/2$ + $\frac{1}{x}$ $1/x$ = $\frac{51}{x}$ $51/x$

Place on a common denominator:

$\frac{x (x)}{2 (x)}$ $(x(x))/(2(x))$ + $\frac{1 (2)}{2 (x)}$ $(1(2))/(2(x))$ = $\frac{51 (2)}{2 (x)}$ $(51(2))/(2(x))$

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

$x^{2}$ $x^2$ + 2 = 102

$x^{2}$ $x^2$ - 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:

A third of a number added to four times the number's reciprocal is equal to half the quotient of 104 and the number.