Question

What are the roots for x^2+47=3 2x^2+50=4 2x^2+85=7

Answer 1

$x^2+47=3\ \ \ |-47\\x^2=-44\\if\ x\in\mathbb{R}\ then\ x\in\O\\if\ x\in\mathbb{C}\ then\ x=\sqrt{-44}=i\sqrt{44}=i\sqrt{4\cdot11}=\boxed{2\sqrt{11}i}\\---------------------------\\2x^2+50=4\ \ \ |-50\\2x^2=-46\ \ \ \ |:2\\x^2=-23\\if\ x\in\mathbb{R}\ then\ x\in\O\\if\ x\in\mathbb{C}\ then\ x=\sqrt{-23}=\boxed{\sqrt{23}i}\\---------------------------\\2x^2+85=7\ \ \ |-85\\2x^2=-78\ \ \ \ |:2\\x^2=-39\\if\ x\in\mathbb{R}\ then\ x\in\O\\if\ x\in\mathbb{C}\ then\ x=\sqrt{-39}=\boxed{\sqrt{39}i}$