SOLUTION: can you please help me solve and check this promblem: (((The sum of a number and its reciprocal is 10/3. What is the number?)))

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Question 152845This question is from textbook Algebra structure and method book 1
: can you please help me solve and check this promblem: (((The sum of a number and its reciprocal is 10/3. What is the number?))) This question is from textbook Algebra structure and method book 1

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Call the number N.
N%2B1%2FN=10%2F3
3N%2B3%2FN=10Multiply both sides by 3.
3N%5E2%2B3=10NMultiply both sides by N.
3N%5E2-10N%2B3=0Bring everything over to one side.
%283N-1%29%28N-3%29=0Factor the quadratic equation.
First solution:
%283N-1%29=0
3N=1
highlight%28N=1%2F3%29
Second solution:
N-3=0
highlight%28N=3%29