Question

Solve (1/x) + x =(1/2) Any help? I'm not sure how to solve this.

Answer 1

Write down that x cannot be zero, then multiply by x.

Answer 2

Lol. Hero is a 99. He gave you the correct answer.

Answer 3

Can you give me step by step directions, please?

Answer 4

Hero gave you step by step directions.

Answer 5

Or, you can just think about it, instead,

x and 1/x are reciprocals.

Example. 4 and 1/4 or 6 and 1/6

Funny thing about reciprocals, ONE of them MUST be AT LEAST 1. So, you add up something that is at least 1, plus a little more, it is unlikely that you will find 1/2 in the mix. x + 1/x >= 1

Answer 6

Unless, of course, you can use complex numbers. Then we're in business.

Answer 7

So like (1/x) and x = (x/1)?

Answer 8

@tkhunny He isn't in that high of a math level. Lol.

Answer 9

You'd confuse him so much with complex numbers/solutions.

Answer 10

Are you calling me stupid?

Answer 11

No, not at all. The level of math you are doesn't include complex numbers/solutions.

Answer 12

Try it out. Pick some numbers

1
2
3
4
5
6
7

Find their reciprocals

1 1/1
2 1/2
3 1/3
4 1/4
5 1/5
6 1/6
7 1/7

Add the two

1 + 1/1 = 2
2 + 1/2 = 5/2 = 2.5
3 + 1/3 = 10/3 = 3.3333...
4 + 1/4 = 17/4 = 4.25
5 + 1/5 = 26/5 = 5.2
6 + 1/6 = 37/6 = 6.166666...
7 + 1/7 = 50/7 = 7.1428571...

We didn't get anywhere near 1/2 or eve 1, did we?

Answer 13

1=(1/1)+ (1/1) =(2/2)?

Answer 14

That makes no sense. 1 is not equal to 2, no matter what you do in the middle. Just a number and its reciprocal. That's all you get.

Answer 15

1 =1/1 sorry.

So if you add 1 + (1/1) = (2/2)?

Answer 16

No, if youadd 1 + 1/1, you get 2/1 = 2,not 1.

Answer 17

Oh

Answer 18

So 2 would be (1/2) and not (2/1)?

Answer 19

A positive number and it's reciprocal. One must be greater than 1 and the other must be less than 1 (except for 1, when they are the same.)

2 has reciprocal 1/2

Adding 2 and 1/2 is like this \(2 + \dfrac{1}{2} = \dfrac{4}{2} + \dfrac{1}{2} = \dfrac{4+1}{2} = \dfrac{5}{2} = 2.5\)

Common Denominator stuff, right?

Answer 20

2 IS 2/1

2's reciprocal is 1/2

Answer 21

Okay. Sorry. I wasn't thinking right.

Answer 22

I understand now.

Answer 23

Solution to the problem?

x + 1/x = 1/2

Algebra and prove that it has No Real Solution. Hero did a good job showing you this, earlier.

Logic and demonstrate that there can be no such solution in the Real Numbers.

Unique solutions don't care how you find them.

Answer 24

(1/x) + (x/x) = (1x/x^2)?

Answer 25

Or is that wrong?

Answer 26

\(\dfrac{1}{x} + x = \dfrac{1}{2}\)

If we really want to find a common denominator.

\(\dfrac{1}{x} + \dfrac{x^{2}}{x} = \dfrac{x}{2x}\)

Almost. One more try.

\(\dfrac{2}{2x} + \dfrac{2x^{2}}{2x} = \dfrac{x}{2x}\)

There it is.

Take a close look at your middle term.

You started with x and changed it to x/x. Since x/x = 1, this is a very different expression. That is no good.

If you were MULTIPLYING the fractions, \(\dfrac{1}{x}\cdot\dfrac{x}{x} = \dfrac{x}{x^{2}}\), but that's a whole different planet.

Answer 27

So it is better to multiply it?

Answer 28

Better? Who cares! What does the problem require? It is not a good question.

\(\dfrac{1}{x} + \dfrac{x}{x} = \dfrac{1+x}{x}\) - The denominator doesn't change on addition.