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=√(-44)=i√(44)=i√(4\cdot11)=\boxed{2√(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=√(-23)=\boxed{√(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=√(-39)=\boxed{√(39)i}`