Solve the equation, and check the solutions 3√(x+2) + √(x-4)=0.

Answer:No solution Step-by-step explanation:Given that,[tex]3\sqrt{x+2}+\sqrt{x-4}=0[/tex]Box x under square root. Inside the square root number must be positive. Therefore, [tex]x+2\geq 0[/tex][tex]x\geq -2[/tex][tex]x-4\geq0[/tex][tex]x\geq4[/tex][tex]3\sqrt{x+2}+\sqrt{x-4}=0[/tex][tex]3\sqrt{x+2}=-\sqrt{x-4}[/tex]Taking square both sides [tex](3\sqrt{x+2})^2=(-\sqrt{x-4})^2[/tex][tex]9(x+2)=(x-4)[/tex][tex]9x+18=x-4[/tex][tex]9x-x=-4-18[/tex][tex]8x=-22[/tex][tex]x=-\dfrac{11}{4}[/tex]Now take intersection of all three solution. [tex]x=-\dfrac{11}{4}[/tex],[tex]x\geq4[/tex],[tex]x\geq -2[/tex]No intersection value of x No solution