Question

a number which exceeds its reciprocal by 3​

Answer 1

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