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

1 Answer
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.