Question

If \(\LARGE{x^2=\frac{1}{x^2}+1}\), then \(\LARGE{x^2+\frac{1}{x^2}=?}\)

Answer 1

@hartnn @ParthKohli @ajprincess plz help :)

Answer 2

\[\dfrac{1}{x^2} = x^2 - 1 \ \ \ \ \]So,\[x^2 + x^2 - 1 = 2x^2 -1\]

Answer 3

Should it be a number value?

Answer 4

\[\Huge{\color{red}{Ans.-\sqrt{5}}}\]

Answer 5

x^4 = x^2 + 1

x^4 - x^2 - 1 = 0

put y = x^2

Answer 6

wait..

Answer 7

That's a quartic equation in \(x\). So multiply through \(x^2\).\[x^4 = x^2 + 1\]

Answer 8

from where do u gt x^4?

Answer 9

I had typed a long explanation, but Yahoo! spilled the beans =P

Answer 10

Solve the given Equation @jiteshmeghwal9 x^2 = 1 + 1/x^2

Answer 11

\(x^2 = 1 + \dfrac{1}{x^2}\) is what you have. Multiply \(x^2\) to both sides.

Answer 12

x^4=x^2+1

Answer 13

That...

Answer 14

Oops sorry i misread it

Answer 15

AArgh.... I'm going to be crazy :(

Answer 16

Sorry dudes but i'm nt getting the right thing :(

Answer 17

Need help

Answer 18

x^4-x^2-1=0
put x^2=t
t^2-t-1=0 solve it

Answer 19

using quadratic formula ?

Answer 20

yep

Answer 21

\[{1 \pm \sqrt{1+4}\over2}={1 \pm \sqrt{5}\over2}\]

Answer 22

No.. i'm nt getting answer

Answer 23

substitute for x^2 in the expression needed

Answer 24

Hm..Hm...After Solving i got sqrt5

Answer 25

can anybody give me steps to the solution, i'm getting confused :((((

Answer 26

hey substitute x^2= (1-sqrt(5))/2 in the expression u get the answer -sqrt(5)

Answer 27

ok

Answer 28

@jiteshmeghwal9 ..Can u Check...ur Solution

Answer 29

Is it sqrt5 or -sqrt5

Answer 30

x^2 + 1 / x^2 = (x^4 + 1) / x^2

Answer 31

\[x^4 -x^2 - 1 = 0 \]We can let \(t = x^2\).\[t^2 - t - 1 = 0 \iff \boxed{t = \dfrac{1\pm \sqrt 5}{2}}{}\]

Answer 32

x^4=x^2+1



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

Answer 33

\[x^2=1/x^2+1\\x^4=1+x^2\\x^4-x^2-1=0\]by quadratic formula,\[x^2=\frac{1\pm \sqrt{5}}{2}\]disregard \(\displaystyle x^2= \frac{1-\sqrt{5}}{2}\) since this is not a real number

Answer 34

nw put the value of x^2

Answer 35

well \(\sqrt{5}=\pm\sqrt{5}\) but in my book it is only given \(\sqrt{5}\) as answer :)

Answer 36

Lol....Then...Go By My method

Answer 37

ohh! k

Answer 38

1 + 2/x^2

1 + 4 / (1 + sqrt5)

(5 + sqrt5)/ (1 + sqrt5) rationalize...

u will get (4 sqrt 5)/4 = sqrt5

Answer 39

Nw u Got it...:)

Answer 40

A little doubt here, just last doubt

Answer 41

Wat?@jiteshmeghwal9

Answer 42

(x^2+2) / x^2 = 1 + 2/x^2 how did u gt this ?

Answer 43

\[x^2=\frac{1+\sqrt 5}{2}\\\frac{1}{x^2}=\frac{2}{1+\sqrt 5}\cdot\frac{1-\sqrt 5}{1-\sqrt 5}=-\frac{1}{2}+\frac{\sqrt 5}{2}\\x^2+\frac{1}{x^2}=(1/2+\sqrt 5/2)+(-1/2+\sqrt 5/2)=\sqrt {5}\]

Answer 44

\[\dfrac{x^2 + 2}{x^2} = \dfrac{x^2}{x^2} + \dfrac{2}{x^2}\cdots\]

Answer 45

I m just gt confused just like my bro @maheshmeghwal9 :(

Answer 46

Oh...i just Did to make calculation easy....if u dont get it...Go My The method used by sirm

Answer 47

Well...now i gt it, thanx all of u a lot :)

Mainly @Yahoo! thanx buddy ;)

Answer 48

Well..)) .welcome