SOLUTION: Twice a number +3 times it’s reciprocal is seven. Find the number

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Question 1135796: Twice a number +3 times it’s reciprocal is seven. Find the number
Found 3 solutions by josgarithmetic, MathLover1, ikleyn:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
n, "a number"

?

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Twice a number +3 times it’s reciprocal is seven. Find the number
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2%283%29%2A%281%2Fn%29=7
?


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Twice a number PLUS 3 times it’s reciprocal is seven. Find the number
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2n%2B3%2Fn=7

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let a number be x
then it’s reciprocal is 1%2Fx

Twice a number:2x
+3 times it’s reciprocal: 2x%2B3%281%2Fx%29
is seven:2x%2B3%281%2Fx%29=7

2x%2B3%281%2Fx%29=7............solve for x

2x%2B3%2Fx=7........both sides multiply by x
2x%5E2%2B3=7x
2x%5E2-7x%2B3=0
2x%5E2-x-6x%2B3=0
%282x%5E2-x%29-%286x-3%29=0
x%282x-1%29-3%282x-1%29=0
%28x+-+3%29+%282+x+-+1%29+=+0
solutions:
x=3
x=1%2F2




Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.
Twice a number +3 times it’s reciprocal is seven. Find the number
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            Your formulation is  TOTALLY  WRONG  since you  INCORRECTLY  USE  " it's ".

            The correct formulation is

              Twice a number +3 times  its reciprocal  is seven. Find the number

            It seems to me that it was explained  MANY  TIMES  to you in this forum.
            Why you still did not learn it ?


Solution

2x + 3%2Fx = 7    ===================>


2x^2 + 3 = 7x  ===================>


2x^2 - 7x + 3 = 0


x%5B1%2C2%5D = %287+%2B-+sqrt%287%5E2+-+4%2A2%2A3%29%29%2F%282%2A2%29 = %287+%2B-+sqrt%2849-24%29%29%2F4 = %287+%2B-+5%29%2F4.


There are two answers:  The number   3  and  the number  1%2F2.