Question

Solution of x^4+1=0 in real numbers

Answer 1

convert into quadratic and see for yourself if solution is possible ..
i.e. let x^2 = y

then y^2 +1 =0
easier to tell now??
well was easier earlier also..

Answer 2

transpose 1 to RHS first

Answer 3

what do you get?

Answer 4

@wazim please reply

Answer 5

x^4+1=0
x^4=-1
Since there is no real number that will give -1 its power is raised to 4.

Answer 6

So what do u think?

Answer 7

i didnt get what is meant to take transpose of equatiom

Answer 8

transpose means like this:
\[\large{x^4+1=0}\]
\[\large{x^4+1-1=0-1}\]

Answer 9

can you tell me what will u get as a simplified form?

Answer 10

transpose 1 to RHS means : subtract 1 both sides

what do you get @wazim ?

Answer 11

\[x^{4}-1=-2\]

Answer 12

what is 1-1 ?

Answer 13

oh yes its zero. and x^4 =-1. so no solution in reals

Answer 14

right :
\[\large{x^4=-1}\]
\[\large{\sqrt[4]{x^4}=\sqrt[4]{-1}}\]

Answer 15

what do you get now @wazim ?

Answer 16

Complex number

Answer 17

x = ?

Answer 18

\[\large{x=(-1)^{\frac{1}{4}}}\]
\[\large{x=((-1)^{\frac{1}{2}})^{\frac{1}{2})}}\]
\[\large{x=i^{\frac{1}{2}}}\]
\[\large{x=\sqrt{i}}\]

M i right?

Answer 19

YES

Answer 20

so that is ur answer

Answer 21

can we resolve it into partial fraction \[\frac{ 1 }{ x^{4}+1 }\]