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

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

Answer»

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

Discussion