Rút gọn:
\(A=\frac{x^2+5x+6+x\sqrt{9-x^2}}{3x-x^2+\left(x+2\right).\sqrt{9-x^2}}\)
\(B=\frac{x^2-5x+6+3\sqrt{x^2-6x+8}}{3x-12+\left(x-3\right).\sqrt{x^2-6x+8}}\)
\(C=\frac{\sqrt{2\sqrt{4-x^2}}.\left(\sqrt{\left(2+x\right)^3}-\sqrt{\left(2-x\right)^3}\right)}{4+\sqrt{4-x^2}}\)
Mọi người ởi giả hộ em bài này đi:
1. Gpt:
a. \(2\left(x^2+2\right)=5\sqrt{x^3+1}\)
b. \(2\left(x^2-3x+2\right)=3\sqrt{x^3+8}\)
c. \(2\left(3x+5\right)\sqrt{x^2+9}=3x^2+2x+30\)
\(\sqrt[3]{x^2-1}+\sqrt{3x^3-2}=3x-2\)
\(\sqrt{\left(2-x\right)\left(5-x\right)}=x+\sqrt{\left(2-x\right)\left(10-x\right)}\)
Giải phương trình:
a. \(3\sqrt{8x}-\sqrt{32x}+\sqrt{50x}=21\)
b. \(\sqrt{25x+50}+3\sqrt{4x+8}-2\sqrt{16x+32}=15\)
c. \(\sqrt{\left(x-2\right)^2}=12\)
d. \(\sqrt{x^2-6x+9}-3=5\)
e.\(\sqrt{\left(2x-1\right)^2}-x=3\)
f. \(\sqrt{3x-6}-x=-2\)
h. \(\sqrt{3-2x}-2=x\)
Giải hệ phương trình : \(\left\{{}\begin{matrix}x^3-y^3-6x^2+13x-y=10\\\sqrt{2x+y+5}-\sqrt{3-x-y}=\left(2x-5\right)y+2\end{matrix}\right.\)
\(3\sqrt{x^3+8}=2\left(x^2-3x+2\right)\)
Rút gon A=\(\sqrt[3]{\dfrac{x^3-3x+\left(x^2-1\right)\sqrt{x^2-4}}{2}}+\sqrt[3]{\dfrac{x^3-3x-\left(x^2-1\right)\sqrt{x^2-4}}{2}}\)
Giải các phương trình:
a) \(x^2+6x-3=4x\sqrt{2x-1}\)
b) \(3x^2+4x-3=4x\sqrt{4x-3}\)
c) \(3x^2+2x+7=3\left(x+1\right)\sqrt{x^2+3}\)
d) \(6x^2+4x+8=5\left(x+1\right)\sqrt{2x^2+3}\)
e)\(6x^2-x=21+\left(x-3\right)\sqrt{x^2+x-6}\)
Tìm x biết:
a.\(\sqrt{18x}+2\sqrt{8x}-3\sqrt{2x}=12\)
b.\(\sqrt{9x+18}+2\sqrt{36x+72}-\sqrt{4x+8}=26\)
c.\(\sqrt{\left(x-2\right)^2}=10\)
d.\(\sqrt{9x^2-6x+1}=15\)
e.\(\sqrt{3x+4}=3x-8\)