a)Giải các phương trình sau bằng phương pháp đặt ẩn phụ:
1) \(x^2-3x-3=\frac{3\left(\sqrt[3]{x^3-4x^2+4}-1\right)}{1-x}\) ;2)\(1+\frac{2}{3}\sqrt{x-x^2}=\sqrt{x}+\sqrt{1-x}\)
b) Giải các phương trình sau(không giới hạn phương pháp):
1)\(2\left(1-x\right)\sqrt{x^2+2x-1}=x^2-2x-1\) ; 2)\(\sqrt{2x+4}-2\sqrt{2-x}=\frac{12x-8}{\sqrt{9x^2+16}}\)
3)\(\frac{3x^2+3x-1}{3x+1}=\sqrt{x^2+2x-1}\) ; 4) \(\frac{2x^3+3x^2+11x-8}{3x^2+4x+1}=\sqrt{\frac{10x-8}{x+1}}\)
5)\(13x-17+4\sqrt{x+1}=6\sqrt{x-2}\left(1+2\sqrt{x+1}\right)\);
6)\(x^2+8x+2\left(x+1\right)\sqrt{x+6}=6\sqrt{x+1}\left(\sqrt{x+6}+1\right)+9\)
7)\(x^2+9x+2+4\left(x+1\right)\sqrt{x+4}=\frac{5}{2}\sqrt{x+1}\left(2+\sqrt{x+4}\right)\)
8)\(8x^2-26x-2+5\sqrt{2x^4+5x^3+2x^2+7}\)
Giaỉ hệ phương trình :
\(\hept{\frac{\frac{1}{3x}+\frac{2x}{3y}=\frac{x+\sqrt{y}}{2x^2+y}\left(1\right)}{\sqrt{y+\sqrt{y}+x+2}+\sqrt{3x+1}=5\left(2\right)}}\)
\(\left(5\right)\sqrt{x+3-4\sqrt{x-1}}\sqrt{x+8+6\sqrt{x-1}}=5\)
\(\left(6\right)2x^2+3x+\sqrt{2x^2+3x+9}=33\)
\(\left(7\right)\sqrt{3x^2+6x+12}+\sqrt{5x^4-10x^2+30}=8\)
\(\left(8\right)x+y+z+8=2\sqrt{x-1}+4\sqrt{y-2}+6\sqrt{z-3}\)
Giải các phương trình vô tỉ sau: (chú ý làm theo pp nhân lượng liên hơp)
a) \(3\left(2+\sqrt{x-2}\right)=2x+\sqrt{x+6}\)
b) \(\sqrt{\frac{42}{5-x}}+\sqrt{\frac{60}{7-x}}=6\)
c) \(\sqrt{x+1}+\sqrt{1-x}=2-\frac{x^2}{4}\)
d) \(4\left(x+1\right)^2=\left(2x+10\right)\left(1-\sqrt{2x+3}\right)^2\)
Rút gọn
a.\(\left(2\sqrt{x}+\sqrt{2x}\right)\left(\sqrt{x}-\sqrt{2x}\right)\)
b. \(\left(\sqrt{3x}+\sqrt{2x}\right)\left(3\sqrt{x}-\sqrt{6x}\right)\)
c.\(\left(\frac{4}{3}\sqrt{3}+\sqrt{2}\sqrt{3\frac{1}{3}}\right)\left(\sqrt{1,2}+\sqrt{2}-4\sqrt{\frac{1}{3}}\right)-2\)
d.\(\left(2\sqrt{x}+\sqrt{y}\right)\left(3\sqrt{x}-2\sqrt{y}\right)\)(x,y lớn hơn hoặc bằng 0)
e.\(\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{x}\sqrt{y}+\sqrt{y}\right)\) (x,y lớn hơn hoặc bằng 0)
Giải các phương trình sau: (hệ phương trình)
1.\(\sqrt{3x^2+6x+7}+\sqrt{5x^2+10x+14}=4-2x-x^2\)
2.\(\sqrt{3-4x}+\sqrt{4x+1}=-16x^2-8x+1\)
3. \(\sqrt{x^2-2x+5}+\sqrt{x+1}=2\)
4. \(\left(-4x-1\right)\sqrt{x^2+1}=2x^2+2x+1\)
5. \(\sqrt{-4x-1}+\sqrt{4x^2+8x+3}=-4x^2-4x\)
6. \(\left(x-3\right)\left(x+1\right)+4\left(x-3\right)\sqrt{\frac{x+1}{x-3}}=-3\)
7. \(\sqrt{x\left(x-1\right)}+\sqrt{x\left(x+2\right)}=2\sqrt{x^2}\)
Ai làm được 4 bài hoặc nhiều hơn mik sẽ tick nha :)
P=\(\left(\frac{\sqrt{x}+1}{\sqrt{2x}+1}+\frac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}-1\right):\left(1+\frac{\sqrt{x}+1}{\sqrt{2x}+1}-\frac{\sqrt{2x}-\sqrt{x}}{\sqrt{2x}-1}\right)\)
=\(\frac{\left(\sqrt{x}+1\right)\left(\sqrt{2x}-1\right)}{\left(\sqrt{2x}+1\right)\left(\sqrt{2x}-1\right)}+\frac{\left(\sqrt{2x}+\sqrt{x}\right)\left(\sqrt{2x}+1\right)}{MTC}-\frac{2x-1}{MTC}\)
=\(\frac{x\sqrt{2}-\sqrt{x}+\sqrt{2x}-1+2x+\sqrt{2x}+x\sqrt{2}+\sqrt{x}-2x+1}{MTC}\)
=\(\frac{2x\sqrt{2}+2\sqrt{2x}}{MTC}\)
Rút gọn
a)\(\sqrt{75}+\sqrt{75}-\)\(\sqrt{192}\)
b)3\(\sqrt{2x}-5\sqrt{2x}-5\sqrt{2x}+9-6\sqrt{2x}\left(x>0\right)\)
c)3\(\sqrt{2x}-4\sqrt{8x}-5\sqrt{50x}\left(x>0\right)\)
d)\(\frac{1}{x^2-y^2}.\sqrt{\frac{2\left(x+y\right)^2}{3}}\left(x\ge0;y\ge0;x\ne y\right)\)
e)\(\left(3\sqrt{2}+\sqrt{3}\right).\sqrt{2}\sqrt{54}\)
f)\(2\sqrt{21}-\left(\sqrt{28}+\sqrt{12}-\sqrt{7}\right).\sqrt{7}\)
1)\(7\sqrt{3x-7}+\left(4x-7\right)\sqrt{7-x}=32\)
2)\(4x^2-11x+6=\left(x-1\right)\sqrt{2x^2-6x+6}\)
3)\(9+3\sqrt{x\left(3-2x\right)}=7\sqrt{x}+5\sqrt{3-2x}\)
4)\(\sqrt{2x^2+4x+7}=x^4+4x^3+3x^2-2x-7\)
5)\(\frac{6-2x}{\sqrt{5-x}}+\frac{6+2x}{\sqrt{5+x}}=\frac{8}{3}\)
6)\(2\left(5x-3\right)\sqrt{x+1}+\left(x+1\right)\sqrt{3-x}=3\left(5x+1\right)\)
7)\(\sqrt{7x+7}+\sqrt{7x-6}+2\sqrt{49x^2+7x-42}=181-14x\)