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

b)\(x^2+x+12\sqrt{x+1}=36\)

c)\(3x-1+\frac{x-1}{4x}=\sqrt{3x+1}\)

d)\(\sqrt{x^2+12}-3x=\sqrt{x^2+5}-5\)

e)\(4x^2+12+\sqrt{x-1}=4\left(x\sqrt{5x-1}+\sqrt{9-5x}\right)\)

f)\(4x^3-25x^2+43x+x\sqrt{3x-2}=22+\sqrt{3x-2}\)

g)\(2\left(x+1\right)\sqrt{x}+\sqrt{3\left(2x^3+5x^2+4x+1\right)}=5x^3-3x^2+8\)

h)\(\sqrt{x^2+12}-\sqrt{x^2+5}=3x-5\)

i)\(\sqrt{1-3x}-\sqrt[3]{3x-1}=\left|6x-2\right|\)

k)\(\sqrt{2x^3+3x^2-1}=2x^2+2x-x^3-1\)

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

a.\(\sqrt{3x+5}\)+\(\sqrt{7-3x}\)=\(9x^2-36x+38\)

b.\(\sqrt[3]{\left(5x+1\right)^2}\)+\(\sqrt[3]{\left(5x-1\right)^2}\)=\(1-\sqrt{25x^2-1}\)

c.\(\sqrt{1+\frac{6}{x+1}}\)+\(8=2x^2+\sqrt{2x-1}\)

d.\(\sqrt{3x^2-7x+3}\)\(-\sqrt{x^2-2}\)\(=\sqrt{3x^2-5x-1}\)\(-\sqrt{x^2-3x+4}\)

e.\(\left(x+2\right)\left(x+4\right)+5\left(x+2\right)\sqrt{\frac{x+4}{x+2}}\)\(=2\)

f.\(\sqrt{x^3-4}\)\(=\sqrt[3]{x^2+4}\)

Giải các pt sau:

a) \(\sqrt{x+8}+\frac{9x}{\sqrt{x+8}}-6\sqrt{x}=0\)

b) \(x^4-2x^3+\sqrt{2x^3+x^2+2}-2=0\)

c) \(3x\sqrt[3]{x+7}\left(x+\sqrt[3]{x+7}\right)=7x^3+12x^2+5x-6\)

d) \(4x^2+\left(8x-4\right)\sqrt{x}-1=3x+2\sqrt{2x^2+5x-3}\)

e) \(16x^2+19x+7+4\sqrt{-3x^2+5x+2}=\left(8x+2\right)\left(\sqrt{2-x}+2\sqrt{3x+1}\right)\)

f) \(\left(5x+8\right)\sqrt{2x-1}+7x\sqrt{x+3}=9x+8-\left(x+26\right)\sqrt{x-1}\)

g) \(\sqrt[3]{3x+1}+\sqrt[3]{5-x}+\sqrt[3]{2x-9}-\sqrt[3]{4x-3}=0\)

Giải phương trình:

1, \(\sqrt{x^2+2x}+\sqrt{2x-1}=\sqrt{3x^2+4x+1}\)

2, \(x^3-3x^2+2\sqrt{\left(x+2\right)^3}-6x=0\)

3, \(2x^3-x^2-3x+1=\sqrt{x^5+x^4+1}\)

4, \(5\sqrt{x^4+8x}=4x^2+8\)

5, \(\left(x^2+4\right)\sqrt{2x+4}=3x^2+6x-4\)

6, \(\left(x^2-6x+11\right)\sqrt{x^2-x+1}=2\left(x^2-4x+7\right)\sqrt{x-2}\)

hộ e vs ak

Giải các pt vô tỉ sau ( bằng phương pháp đặt ẩn phụ đưa về phương trình tích )

a) \(\sqrt{x^3+x^2+3x+3}+\sqrt{2x}=\sqrt{x^2+3}+\sqrt{2x^2+2x}\)

b) \(\sqrt{x^2-3x}+2\sqrt{x}-4\sqrt{x-3}-x+8=0\)

c) \(\left(5x^2+4x+3\right)\sqrt{x}=\left(x+3\right)\sqrt{5x^2+4x}\)

d) \(\left(x+2\right)\sqrt{3x+\frac{1}{x}}=3x^2+3\)

e)\(\left(x^2+2x+1\right)3\sqrt{x^2+\frac{3}{x}}=x^3+2x^2+5\)

Giai phuong trinh

1/ \(\sqrt{x^2+4x+5}+\sqrt{x^2-6x+13}=3\)

2/ \(\sqrt{3x^2-18x+28}+\sqrt{4x^2-24x+45}=6x-x^2-5\)

3/ \(\sqrt{2x^2-4x+27}+\sqrt{3x^2-6x+12}=4x^2+8x+4\)

4/ \(\sqrt{x^2+x+7}+\sqrt{x^2+x+2}=\sqrt{3x^2+3x+19}\)

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

6/ \(\left(x+4\right)\left(x+1\right)-3\sqrt{x^2+5x+2}=6\)

7/ \(\sqrt{2x^2+3x+5}+\sqrt{2x^2-3x+5}=3\sqrt{x}\)

Giải phương trình

1 .\(2x+1+\sqrt{x+3}-\sqrt{x}=\)\(2\sqrt{x^2+3x}\)

2.\(10x^2+3x+1=\)\(\sqrt{x^2+3}\left(1+6x\right)\)

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

4.\(x^2+3x+4=\left(x+3\right)\sqrt{x^2+x+2}\)

5.\(2\sqrt{x+3}=9x^2-x-4\)

6.\(12\sqrt{x}+2\sqrt{x-1}=3x+9\)

Phương trình vô tỉ:

1Giải các phương trình vô tỉ:

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

b)\(\sqrt{X-1}-\sqrt{5X-1}=\sqrt{3X-2}\)

2.\(\sqrt{\left(X-1\right)X}+\sqrt{\left(X-2\right)X}=\sqrt{\left(X+3\right)X}\)

3.\(2\sqrt{2X-1}=X^2-2X\)

4a).\(\sqrt{X^2+X-12}=8-X\)

b)\(\sqrt{x^2-x-8}=\sqrt{4-2x}\)

5.\(\sqrt{x+1}+\sqrt{x}=\sqrt{x+2}\)

Mong mọi người giúp nha ♥♥♥ Toàn bộ 5 bài đều là giải phương trình vô tỉ ạ.

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)\(\sqrt{7x+7}+\sqrt{7x-6}+2\sqrt{49x^2+7x-42}=181-14x\)