Question

Tan^2x+3=0

Answer 1

Is it \[
\tan^2 (x) + 3 = 0 \:?
\]

Answer 2

if so, what do you think about \(\tan^2(x) = -3\) ?

Answer 3

tan2(x)=−3


$\mathrm{Let:\:}\tan\left(x\right)=u$Let: tan(x)=u

$u^2=-3$u2=−3




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$u^2=-3\quad:\quad u=i\sqrt{3},\:u=-i\sqrt{3}$u2=−3 : u=i√3, u=−i√3


$\mathrm{Substitute\:back}\:u=\tan\left(x\right)$Substitute back u=tan(x)

$\tan\left(x\right)=i\sqrt{3},\:\tan\left(x\right)=-i\sqrt{3}$tan(x)=i√3, tan(x)=−i√3




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$\tan\left(x\right)=i\sqrt{3}\quad:\quad\mathrm{No\:Solutions}$tan(x)=i√3 : No Solutions



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$\tan\left(x\right)=-i\sqrt{3}\quad:\quad\mathrm{No\:Solutions}$tan(x)=−i√3 : No Solutions


$\mathrm{Combine\:all\:the\:solutions}$Combine all the solutions

$\mathrm{No\:Solutions}$No Solutions

Answer 4

When you look at \(Y^2 = -3\), you see that there is no solution \(Y\in \mathbb{R}\).
Here \(Y=\tan(x)\). -> whatever \(x\), the square of \(Y=\tan(x)\) is some positive value and it can't be equal to \(-3\).