SOLUTION: The sum of non zero number an twice it's reciprocal is 33/4 find the number

Question 1102520: The sum of non zero number an twice it's reciprocal is 33/4 find the number
Found 4 solutions by josgarithmetic, Theo, greenestamps, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
The description as an equation:

(factorable)
.
.

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
if x is the number, then the reciprocal of x is 1/x.
2 times the reciprocal of x is 2/x.

x + 2/x = 33/4
multiply both sides of this equation by 4x to get 4x^2 + 8 = 33x

subtract 33x from both sides of this equation and re-order the terms in descending order of degree to get 4x^2 - 33x + 8 = 0

factor this quadratic equation to get(4x-1) * (x-8) = 0
solve for x to get x = 1/4 or x = 8

when x = 1/4, the reciprocal of x is equal to 4 and 2 times the reciprocal of x is equal to 8.
x + 2/x becomes 1/4 + 8 which becomes 1/4 + 32/4 which is equal to 33/4.

when x = 8, the reciprocal of x is equal to 1/8 and 2 times the reciprocal of x is equal to 2/8 which is equal to 1/4.
x + 2/x becomes 8 + 1/4 which becomes 32/4 + 1/4 which is equal to 33/4.

both solutions are good.
the number can be 1/4 or 8.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

If the sum of a number and twice its reciprocal is the rational number 33/4, then almost certainly the number and its reciprocal are both rational numbers.

33/4 is 8 1/4....

So skip the algebra:

The number and it reciprocal are, in either order, 8 and 1/8.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
8 and 1/4 are the correct answers. The solution by @Theo is complete and correct.

1/8 is not the correct answer. The answer by @greenestamps is not correct.

The solution by @josgarithmetic (giving only 8) is not complete.

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