Các câu hỏi tương tự
Rút gọn:
\(A=\frac{x^2+5x+6+x\sqrt{9-x^2}}{3x-x^2+\left(x+2\right).\sqrt{9-x^2}}\)
\(B=\frac{x^2-5x+6+3\sqrt{x^2-6x+8}}{3x-12+\left(x-3\right).\sqrt{x^2-6x+8}}\)
\(C=\frac{\sqrt{2\sqrt{4-x^2}}.\left(\sqrt{\left(2+x\right)^3}-\sqrt{\left(2-x\right)^3}\right)}{4+\sqrt{4-x^2}}\)
Rút gọn:
\(A=\frac{x^2+5x+6+x\sqrt{9-x^2}}{3x-x^2+\left(x+2\right).\sqrt{9-x^2}}\)
\(B=\frac{x^2-5x+6+3\sqrt{x^2-6x+8}}{3x-12+\left(x-3\right).\sqrt{x^2-6x+8}}\)
\(C=\frac{\sqrt{2\sqrt{4-x^2}}.\left(\sqrt{\left(2+x\right)^3}-\sqrt{\left(2-x\right)^3}\right)}{4+\sqrt{4-x^2}}\)
phương pháp 1 biến đổi về phương trình có chứa dấu giá trị tuyệt đối
1. \(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8+6\sqrt{x-1}}=5\)
2. \(\sqrt{x+2-3\sqrt{2x-5}}+\sqrt{x-2+\sqrt{2x-5}}=2\sqrt{2}\)
3. \(\sqrt{x+\sqrt{6x-9}}+\sqrt{x-\sqrt{6x-9}}=\sqrt{6}\)
4. \(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}=\dfrac{x+8}{5}\)
25. 7\(\sqrt{x}\)- 6x- 2
26.\(x^2\)-\(\sqrt{x}\)+x -1
27. 2a - 5\(\sqrt{ab}\)+ 3b
28.\(\sqrt{ab}\)+2\(\sqrt{a}\)+ 3\(\sqrt{b}\)+6
Phương pháp 3. Sử dụng phép đặt ẩn phụ
a \(3x^2+21x+18+2\sqrt{x^2+7x+7}=2\)
b \(x^2-6x+9=4\sqrt{6-6x+x^2}\)
c \(\sqrt{\dfrac{x^2+x+1}{x}}+\sqrt{\dfrac{x}{x^2+x+1}}=\dfrac{7}{4}\)
d \(x^2+8x-3=2\sqrt{x\left(8+x\right)}\)
Giải các PT sau:
\(a,\sqrt{x-2\sqrt{x-1}}-\sqrt{x-1}=1\)
\(b,\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8+6\sqrt{x-1}}=1\)
\(c,\sqrt{x+\sqrt{2x-1}}+\sqrt{x-\sqrt{2x-1}}=\sqrt{2}\)
\(d,\sqrt{x+\sqrt{6x-9}}+\sqrt{x-\sqrt{6x-9}}=\sqrt{6}\)
Thu gọn
\(\left(\dfrac{6x+4\sqrt{x}}{x\sqrt{x}-4\sqrt{x}}-\dfrac{6}{3\sqrt{x}+6}+1\right):\dfrac{1}{\sqrt{x}-2}\)
1\(\sqrt{5+2\sqrt{8}}-\sqrt{5-2\sqrt{8}}\) 2)\(\dfrac{\sqrt{x^2+2\sqrt{3x}+3}}{x^2-3}\) 3) \(\dfrac{\sqrt{x^2-5x+6}}{\sqrt{x-2}}\) 4)\(\dfrac{\sqrt{\left(x-4\right)^2}}{x^2-5x+4}\) 5) \(\dfrac{3x+1}{\sqrt{9x^2+6x+1}}\)
\(\left(5\right)\sqrt{x+3-4\sqrt{x-1}}\sqrt{x+8+6\sqrt{x-1}}=5\)
\(\left(6\right)2x^2+3x+\sqrt{2x^2+3x+9}=33\)
\(\left(7\right)\sqrt{3x^2+6x+12}+\sqrt{5x^4-10x^2+30}=8\)
\(\left(8\right)x+y+z+8=2\sqrt{x-1}+4\sqrt{y-2}+6\sqrt{z-3}\)