lấy casio ex570 hoặc plus cũng tính đc dấy

a) \(\sqrt{2-x^2+2x}+\sqrt{-x^2-6x-8}=1+\sqrt{3}\)

\(pt\Leftrightarrow\sqrt{-x^2+2x+1+1}+\sqrt{-x^2-6x-9+1}=1+\sqrt{3}\)

\(\Leftrightarrow\sqrt{-\left(x-1\right)^2+1}+\sqrt{-\left(x+3\right)^2+1}=1+\sqrt{3}\)

Dễ thấy: \(VT\le2< 1+\sqrt{3}=VP\) (vô nghiệm)

b)\(\sqrt{9x^2-6x+2}+\sqrt{45x^2-30x+9}=\sqrt{6x-9x^2+8}\)

\(pt\Leftrightarrow\sqrt{9x^2-6x+1+1}+\sqrt{45x^2-30x+5+4}=\sqrt{-9x^2+6x-1+9}\)

\(\Leftrightarrow\sqrt{\left(3x-1\right)^2+1}+\sqrt{5\left(3x-1\right)^2+4}=\sqrt{-\left(3x-1\right)^2+9}\)

Dễ thấy: \(VT\ge1+\sqrt{4}=3=VP\)

Đẳng thức xảy ra khi \(x=\dfrac{1}{3}\)

ĐKXĐ: x∈R

Đặt \(a=9x^2-6x\)

\(\sqrt{9x^2-6x+2}+\sqrt{45x^2-30x+9}=\sqrt{6x-9x^2+8}\)

=>\(\sqrt{a+2}+\sqrt{5a+9}=\sqrt{-a+8}\)

=>\(\sqrt{a+2}-1+\sqrt{5a+9}-2=\sqrt{-a+8}-3\)

=>\(\frac{a+2-1}{\sqrt{a+2}+1}+\frac{5a+9-4}{\sqrt{5a+9}+2}=\frac{-a+8-9}{\sqrt{-a+8}+3}\)

=>\(\frac{a+1}{\sqrt{a+2}+1}+\frac{5a+5}{\sqrt{5a+9}+2}=\frac{-a-1}{\sqrt{-a+8}+3}\)

=>\(\left(a+1\right)\left(\frac{1}{\sqrt{a+2}+1}+\frac{5}{\sqrt{5a+9}+2}+\frac{1}{\sqrt{-a+8}+3}\right)=0\)

=>a+1=0

=>a=-1

=>\(9x^2-6x=-1\)

=>\(9x^2-6x+1=0\)

=>\(\left(3x-1\right)^2=0\)

=>3x-1=0

=>3x=1

=>\(x=\frac13\)

1: Đặt \(a=9x^2-6x\)

=>\(45x^2-30x=5\left(9x^2-6x\right)=5a\)

\(\sqrt{9x^2-6x+2}+\sqrt{45x^2-30x+9}=\sqrt{6x-9x^2+8}\)

=>\(\sqrt{a+2}+\sqrt{5a+9}=\sqrt{-a+8}\)

=>\(\sqrt{a+2}-1+\sqrt{5a+9}-2=\sqrt{-a+8}-3\)

=>\(\frac{a+2-1}{\sqrt{a+2}+1}+\frac{5a+9-4}{\sqrt{5a+9}+2}=\frac{-a+8-9}{\sqrt{-a+8}+3}\)

=>\(\left(a+1\right)\left(\frac{1}{\sqrt{a+2}+1}+\frac{5}{\sqrt{5a+9}+2}+\frac{1}{\sqrt{a+8}+3}\right)=0\)

=>a+1=0

=>a=-1

=>\(9x^2-6x=-1\)

=>\(9x^2-6x+1=0\)

=>\(\left(3x-1\right)^2=0\)

=>3x-1=0

=>3x=1

=>x=1/3

2: Đặt \(x^2-2x=a\)

\(\sqrt{2x^2-4x+3}+\sqrt{3x^2-6x+7}=2-x^2+2x\)

=>\(\sqrt{2\left(x^2-2x\right)+3}+\sqrt{3\left(x^2-2x\right)+7}=-\left(x^2-2x\right)+2\)

=>\(\sqrt{2a+3}+\sqrt{3a+7}=-a+2\)

=>\(\sqrt{2a+3}-1+\sqrt{3a+7}-2=-a+2-3\)

=>\(\frac{2a+2}{\sqrt{2a+3}+1}+\frac{3a+7-4}{\sqrt{3a+7}+2}=-a-1\)

=>\(\left(a+1\right)\left(\frac{2}{\sqrt{2a+3}+1}+\frac{3}{\sqrt{3a+7}+2}+1\right)=0\)

=>a+1=0

=>\(x^2-2x+1=0\)

=>\(\left(x-1\right)^2=0\)

=>x-1=0

=>x=1