The sum of a number and 81 times its reciprocal is - 18. Find the number.
A) -9
B) -90
C) 9
D) 72

Name: The sum of a number and 81 times its reciprocal is - 18. Find the number. A) -9 B) -90 C) 9 D) 72
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Question

Quizplus · Accepted Answer

The equation can be set up as $x + \frac{81}{x} = -18$. Multiplying through by $x$ to clear the denominator gives a quadratic equation: $x^2 - 18x + 81 = 0$. Factoring this equation gives $(x - 9)(x + 9) = 0$, so $x = 9$ or $x = -9$. However, given the sum is negative, the correct answer is $x = -9$.

The Sum of a Number and 81 Times Its Reciprocal