Question

Hello, we have :

(1/x) + x < 2

(1/x) + x = 2 /*x
1 + x^2 = 2x
x^2 - 2x + 1 = 0
(x-1)^2 = 0
x = 1

x < 1

Is this correct ? Becuause wolfram said result is x < 0 ?!

Answer 1

i think its right..

Answer 2

http://www.wolframalpha.com/input/?i=%281%2Fx%29%2Bx%3C2

Answer 3

I will w8 few minutes if somebody else will find mistake. If not will close it with correct answer x < 1

Answer 4

whats the second line...?

Answer 5

linear equation ? just put "=" in place of "<"

Answer 6

of course i can count with "<" but "=" looks more naturally when you solve equation

Answer 7

k.... (1/x+x)<=|2|...was not that the condition

Answer 8

I dont understand you amriju ..

Answer 9

u cannot solve it like that, u need to consider < sign only

Answer 10

(1/x) + x < 2
Let x>0 , u got
(x-1)^2 < 0
which is not possible because a square of a number is always positive

hence x<0

Answer 11

only when x>0, u multiply x on both sides, and u don't flip the sign

Answer 12

It is not clear to me at all..

Answer 13

consider when x<0
so when u multiply x on both sides, u should flip the sign
and u get (x-1)^2 > 0
which confirms x<0

Answer 14

Thanks a lot. But i still dont understand where i put mistake and how i should solve it. I dont understan english at all. I just need time to understand it

Answer 15

Did u know that u should flip the inequality sign when multiplying or dividing by a negative number ? ex. if x>0, -x <0
Your mistake, u cannot just replace < with = and replace it back after solving it.....

Answer 16

will it help if i put all steps together ?

Answer 17

I just know.. that if i multiply it by -1 for example.. i flip the sign of course..

Answer 18

but i just multiply it by x to get 1 + x^2 = 2x

Answer 19

Dont know if you are pointing on this step or not..

Answer 20

yeah, we don't know whether x is positive or negative.
if positive, we need not flip the sign, if negative, we need to flip the sign.
hence, we go for 2 conditions.

Answer 21

Ah ok.. i understand now..

Answer 22

but how this affect that result is x < 0 ? Iam so dumb.. sorry

Answer 23

(1/x) + x < 2
consider (i) x>0 (ii) x<0
u get (x-1)^2 < 0 u get (x-1)^2 < 0
NEVER true, Always true
so x is not greater than 0. hence the inequality (1/x) + x < 2 is
satisfied for all x<0
hence x<0 is solution

Answer 24

Ah, now i understand it. Thanks a lot for detailed description.. ;)

Answer 25

welcome ^_^