Question

a positive number exceeds four times its reciprocal by three, find the number

Answer 1

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

Step-by-step explanation:

hope it helps..

Answer 2

⇒ Let the number be x.

$⇒ Sixty \: - \: five \: times \: of \: its \: reciprocal = \frac{65}{x}$

According to the given condition,

⇒ x− x65=64

⇒ x²-65=64x

⇒ x²−64x−65=0

⇒ x²−65x+x−65=0

⇒ x(x−65)+1(x−65)=0

⇒ (x−65)(x+1)=0

⇒ x−65=0 and x+1=0

∴ x=65 and x=−1