Question

a number which exceeds its reciprocal by 3
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Answer 1

Step-by-step explanation:

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A number exceeds four times its reciprocal by 3. Find the number

Mathematics

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1 Answers

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Ganga Sarin

Grade 12

follow

First we have to convert the given

word problem into algebraic

equation.

Let the number = x

Four times of its reciprocal = 4/ x

According to the problem,

x - 4 / x = 3

( x ^2 - 4 )/ x = 3

x ^2 - 4 = 3x

x ^2 - 3x - 4 = 0

Spilt the middle term

x ^2 + x - 4x - 4 = 0

x ( x + 1 ) - 4 ( x + 1 ) = 0

( x + 1 ) ( x - 4 ) = 0

x + 1 = 0 or x - 4 = 0

x = -1 or x = 4