Dear friends, Please read our latest blog post for an important announcement about the website. ❤, The Socratic Team

The sum of a number and its reciprocal is 17/4. What is the number?

1 Answer
Write your answer here...
Start with a one sentence answer
Then teach the underlying concepts
Don't copy without citing sources
preview
?

Answer

Write a one sentence answer...

Answer:

Explanation

Explain in detail...

Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

13
Apr 1, 2017

Answer:

Solution is number is #4# or #1/4#.

Explanation:

Let the be #x#. Then, its reciprocal is #1/x#.

Therefore we have #x+1/x=17/4#

Multiplying every term by #4x#, we get

#4x xx x+4x xx 1/x=4x xx17/4#

i.e. #4x xx x+4cancelx xx 1/cancelx=cancel4x xx17/cancel4#

or #4x^2+4=17x#

or #4x^2-17x+4=0#

or #4x^2-16x-x+4=0#

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

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

i.e. either #4x-1-0# i.e. #4x=1# and #x=1/4#

or #x-4=0# and #x=4#

Hence, solution is number is #4# or #1/4#.

This is so because not only both of them add up to #17/4#, but also that each is reciprocal of the other one.

Was this helpful? Let the contributor know!
1500
Impact of this question
886 views around the world
You can reuse this answer
Creative Commons License