Bài 2 : Giải các phương trình sau
1 , \(x\left(x+5\right)=2\sqrt[3]{x^2+5x-2}-2\)
2 , \(\sqrt[3]{x+5}+\sqrt[3]{x+6}=\sqrt[3]{2x+11}\)
3 , \(\sqrt[4]{x-\sqrt{x^2-1}}+\sqrt{x+\sqrt{x^2-1}}=2\)
4 , \(x^2-2x-8=4\sqrt{\left(4-x\right)\left(x+2\right)}\)
5 , \(x^2+5x+2+2\sqrt{x^2+5x+10}=0\)
6 , \(\sqrt{2x^2+3x-5}=x+1\)
7 , \(\left(x-1\right)\left(x-3\right)+3\sqrt{x^2-4x+5}-2=0\)
Tìm x:
a.\(\sqrt{4-\sqrt{4+x}}=x\)
b.\(4\left(\sqrt{x-1}-3\right)x^2+\left(13\sqrt{x+1}-8\right)x-4\sqrt{x-1}-3=0\)
c.\(\sqrt{2x-3}+2\sqrt{x-3}\ge3\sqrt[4]{2x^2+x-6}\)
GIẢI PHƯƠNG TRÌNH
1, ĐẶT ẨN PHỤ
A, \(\sqrt{1+x}+\sqrt{8-x}+\sqrt{8-7x+x^2}=3\)
b,\(x^2+x+6+2x\sqrt{x+3}=4\left(x+\sqrt{x+3}\right)\)
2, ĐÁNH GIÁ
a,\(\sqrt{x+1}+\sqrt{x+10}=\sqrt{x+2}+\sqrt{x+5}\)
b,\(\frac{x}{\sqrt{4x-1}}+\frac{\sqrt{4x-1}}{x}=2\)
Giải pt, bất pt
a) \(\left(\sqrt{x+3}-\sqrt{x+1}\right)\left(x^2+\sqrt{x^2+4x+3}=2x\right)\)
b) \(\left(x^2-3x+2\right)\left(x^2-12x+32\right)\le4x^2\)
c) \(2\sqrt{3x+7}-5\sqrt[3]{x-6}=4\)
giải các bất phương trình sau:\(\frac{2x-5}{\left|x-3\right|}+1>0\)
\(\frac{\left|x-2\right|}{x^2-5x+6}>=3\)
\(\sqrt{2x+\sqrt{6x^2+1}}>x+1\)
\(\sqrt{x+3}-\sqrt{7-x}>\sqrt{2x-8}\)
\(\sqrt{2-x}>\sqrt{7-x}-\sqrt{-3-2x}\)
\(\sqrt{2x+3}+\sqrt{x+2}\le1\)
\(\left(x+5\right)\left(x-2\right)+3\sqrt{x\left(x+3\right)}>0\)
Bài 1 : giải các phương trình sau
1 , \(\left(x^2-6x\right)\sqrt{17-x^2}=x^2-6x\)
2 , \(\left(x^2+5x+4\right)\sqrt{x+3}=0\)
3, \(\sqrt{3x}+\sqrt{2x-2}=\sqrt{1-x}+2\)
4, \(\left(x^2-4x+3\right)\sqrt{x-2}=0\)
5 , \(\sqrt{x^2+3x-2}=\sqrt{1+x}\)
6 , \(\left(\sqrt{x-4}-1\right)\left(x^2-7x+6\right)=0\)
7, \(\sqrt{2x^2-8x+4}=x-2\)
8 , \(\sqrt{3x+7}-\sqrt{x+1}=2\)
giải các BPT :
1. \(\sqrt{x^2-3x+2}+\sqrt{x^2-3x+16}>3\)
2.\(\sqrt{2x^2+8x+6}+\sqrt{x^2-1}\le2x+2\)
3.\(\sqrt{2x-1}+\sqrt{3x-2}< \sqrt{4x-3}+\sqrt{5x-4}\)
Tìm GTNN
a) \(y=\sqrt{x^3+2\left(1+\sqrt{x^3+1}\right)}+\sqrt{x^3+2\left(1-\sqrt{x^3+1}\right)}\)
b) \(f\left(x\right)=\dfrac{x}{2}+\dfrac{2}{x-1}\) với x>1
c) \(y=\dfrac{x-2017}{\sqrt{x-2018}}\)
Giải các bất phương trình sau:
1. \(\sqrt{5x+1}-\sqrt{4x-1}< 3\sqrt{x}\)
2. \(\sqrt{x+2}-\sqrt{3-x}< \sqrt{5-2x}\)
3 \(\dfrac{\sqrt{12+x-x^2}}{x-11}\ge\dfrac{\sqrt{12+x-x^2}}{2x-9}\)
4.\(\sqrt{x^2-8x+15}+\sqrt{x^2+2x-15}\le\sqrt{4x^2-18x+18}\).