Question

Boom Dia Me ajudem só na A e B por favor ^.^

Answer 1

a)
$x^{2} -2x+3=3. \sqrt{ x^{2} -2x+1}\\ \\ \boxed{y= x^{2} -2x }\\ \\ y+3=3. \sqrt{y+1}\\ \\ (y+3)^2=(3. \sqrt{y+1})^2\\ \\ y^2+6y+9=9y+9\\ \\ y^2-3y=0\\ \\ y=0\\ y=3$

$x^2-2x=0\Rightarrow x=0 \ \ ou \ \ x=2\\ \\ x^2-2x=3 \Rightarrow x = -1 \ \ ou \ \ x=3\\ \\ S=\{-1,0,2,3}$

b)
$3^{ \sqrt{3-x} }.3^{- \sqrt{x+2} }=3^{\sqrt{2x-3}}\\ \\ 3^{ \sqrt{3-x}- \sqrt{x+2} }=3^{\sqrt{2x-3}}\\ \\ \sqrt{3-x}- \sqrt{x+2} =\sqrt{2x-3}\\ \\ (\sqrt{3-x}- \sqrt{x+2})^2 =(\sqrt{2x-3})^2\\ \\ 5-2 \sqrt{-x^2+x+6}=2x-3\\ \\ -2 \sqrt{-x^2+x+6}=2x-8$

$(-2 \sqrt{-x^2+x+6})^2=(2x-8)^2\\ \\ 4(-x^2+x+6)=4x^2-32x+64\\ \\ -8 x^2+36 x-40 = 0\\ \\ S=\{2,\frac{5}{2}\}$