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LostInParadise's avatar

Can you find the two solutions of x+1/x = 5.2 in your head?

Asked by LostInParadise (32184points) May 18th, 2020

Something to do during quarantine. For those who immediately say no, you are going to be embarrassed to see how simple the solution is. Hint: What is another way of writing 5.2?

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8 Answers

LostInParadise's avatar

Those are the answers. I hope you solved it the easy way.

tedibear's avatar

No, I can’t. I might manage it on paper.

JeSuisRickSpringfield's avatar

The easy way would be to plug it into Google. I did it in my head.

dxs's avatar

For me, if it’s rational I put it into a ratio. I got to the equation (x^^2+1)/x = 26/5 [x^^2 means x squared] and saw that if the denominators match (x = 5) then so will the numerators. Then, going by the original equation, which tells us it’s the sum of a number and its reciprocal, I knew 1/5 must be the other answer.

I tried working with decimals, too. I got to the polynomial x^^2 – 5.2x + 1 = 0. From here I admit I summoned the integers for a moment and used 10x^^2 – 52x + 10 to help me factor it into (x – 5)(x – 0.2). Integer coefficients helped me find 50 and 2 as opposed to getting 5 and 0.2.

Soubresaut's avatar

The first time I solved it, I’d imagined parentheses around (x + 1). It was simple to step through in my head, but your hint hadn’t helped me much (haha, that should have been my clue).

Then I saw @JeSuisRickSpringfield‘s response, looked back at the question, and realized I’d misread the problem.

And then your hint made sense: x + 1/x = 5 + 1/5

I’m pretty sure I would have gotten 5 without having seen @JeSuisRickSpringfield‘s response, but I’m also pretty sure I would have missed 1/5. (Having seen it as a solution, though, I see how it works.)

LuckyGuy's avatar

I’ll admit it. I immediately stared to solve for it in my head before I saw your hint. I multiplied everything by x and made a polynomial. Then i saw the hint. That clinched it.

ARE_you_kidding_me's avatar

I did it in my head. The .2 was a dead giveaway that X=5

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