Question

SOLVE: √x+√x-3 =3
(roots, radicals, and complex numbers)
THANKS:)

Answer 1

\(\LARGE\color{blue}{ \bf \sqrt{x}+ \sqrt{x-3}=3 }\) square both sides...

\(\LARGE\color{blue}{ \bf x+2(\sqrt{x})( \sqrt{x-3})+ (x-3)=3 }\)

\(\LARGE\color{blue}{ \bf x+2\sqrt{x^2-3x}+ (x-3)=3 }\)

\(\LARGE\color{blue}{ \bf x+2\sqrt{x^2-3x}+ x-3=3 }\)

so afr so good? (about to post more....)

Answer 2

\(\LARGE\color{blue}{ \bf x+2\sqrt{x^2-3x}+ x=6 }\)

\(\LARGE\color{blue}{ \bf 2x+2\sqrt{x^2-3x}=6 }\)

\(\LARGE\color{blue}{ \bf 2(x+\sqrt{x^2-3x})=3(2) }\)

\(\LARGE\color{blue}{ \bf x+\sqrt{x^2-3x}=3 }\)

tell me if you are loosing me...

Answer 3

no i got it

Answer 4

\(\LARGE\color{blue}{ \bf x+\sqrt{x^2-3x}=3 }\)

\(\LARGE\color{blue}{ \bf \sqrt{x^2-3x}=3-x }\)

\(\LARGE\color{blue}{ \bf x^2-3x=9-6x+x^2 }\)

\(\LARGE\color{blue}{ \bf -3x=9-6x }\)

\(\LARGE\color{blue}{ \bf 3x=9 }\)

\(\LARGE\color{blue}{ \bf x=3 }\)

Answer 5

My bad....

Answer 6

I errored in first steps...

Answer 7

oh really? which step?