Question

The sum of a number and its reciprocal is 4.25 .Find the number?Please also give me steps for solving it

Answer 1

Let the number be x,

x +1/x = 4.25

(x² +1)/x = 4.25

x²+1 = 4.25*x

Multiply by 4 on both sides

4x² +4 = 17x

4x² -17x +4 =0

4x² -(16+1)x +4 =0

4x² -16x -x +4 =0

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

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

4x-1 =0 OR x-4 =0

4x =1 Or x=4

x =1/4 Or x=4


Now, the number is 4 OR 1/4

If we take 4, its reciprocal will 1/4

If we take 1/4, its reciprocal will be 4


In both the conditions,

Numbers are 4 and 1/4

So, take any from 4 and 1/4, both will give the same requirements

MAIN ANSWER = 4 as well as 1/4

I hope this will help you



-by ABHAY

Answer 2

Answer:

the answer is 4 or 1/4 for x