`Ta có : \(x=\sqrt[3]{4\sqrt{5}+4}-\sqrt[3]{4\sqrt{5}-4}\)
\(\Rightarrow x^3=8-3\sqrt[3]{\left(4\sqrt{5}\right)^2-4^2}.x\Leftrightarrow x^3+12x-8=0\Rightarrow x^3-12x-9=-1\)
Từ đó tính được P = (-1)2016 = 1
Tính giá trị biểu thức:
a) \(P=\left(x^3+12x-9\right)^{2005}\), biết \(x=\sqrt[3]{4\left(\sqrt{5}+1\right)}-\sqrt[3]{4\left(\sqrt{5}-1\right)}\);
b) \(Q=x^3+ax+b\), biết \(x=\sqrt[3]{-\dfrac{b}{2}+\sqrt{\dfrac{b^2}{4}+\dfrac{a^3}{27}}}+\sqrt[3]{-\dfrac{b}{2}-\sqrt{\dfrac{b^2}{4}+\dfrac{a^3}{27}}}\)
Cho \(x=\sqrt[3]{4\left(\sqrt{5}+1\right)}-\sqrt[3]{4\left(\sqrt{5}-1\right)}\)
Tính giá trị \(P=\left(x^3+12x-9\right)^{2005}\)
\(\sqrt{\left(2x+3\right)^2}=5\)
\(\sqrt{9.\left(x-2\right)^2}=18\)
\(\sqrt{9x-18}-\sqrt{4x-8}+3\sqrt{x-2}=40\)
\(\sqrt{4.\left(x-3\right)^2}=8\)
\(\sqrt{4x^2+12x+9}=5\)
\(\sqrt{5x-6}-3=0\)
Bài Toán :
Giải phương trình sau :
\(\frac{3\left(x-\sqrt{3}\right)\left(x-\sqrt{5}\right)}{\left(1-\sqrt{3}\right)\left(1-\sqrt{5}\right)}+\frac{4.\left(x-1\right)\left(x-\sqrt{5}\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}-\sqrt{5}\right)}+\frac{5\left(x-1\right)\left(x-\sqrt{3}\right)}{\left(\sqrt{5}-1\right)\left(\sqrt{5}-\sqrt{3}\right)}=3x-2\)
\(\left(6\right)\dfrac{3\sqrt{x}}{5\sqrt{x}-1}\le-3\)
\(\left(7\right)\dfrac{8\sqrt{x}+8}{6\sqrt{x}+9}>\dfrac{8}{3}\)
\(\left(8\right)\dfrac{\sqrt{x}-2}{2\sqrt{x}-3}< -4\)
\(\left(9\right)\dfrac{4\sqrt{x}+6}{5\sqrt{x}+7}\le-\dfrac{2}{3}\)
\(\left(10\right)\dfrac{6\sqrt{x}-2}{7\sqrt{x}-1}>-6\)
\(\left(1\right)\sqrt{x^2-9}-2\sqrt{x-3}=0\)
\(\left(2\right)\sqrt{4x+1}-\sqrt{3x-4}=1\)
\(\left(3\right)\sqrt{x^2-10x+25}=5-x\)
\(\left(4\right)\sqrt{x^2-8x+16}=x+2\)
1. Tinh
\(\left(3-\sqrt{2}\right).\sqrt{7+4\sqrt{3}}\)
\(\left(\sqrt{3}+\sqrt{5}\right).\sqrt{7-2\sqrt{10}}\)
\(\left(2+\sqrt{5}\right).\sqrt{9-4\sqrt{5}}\)
\(\left(\sqrt{6}+\sqrt{10}\right)\sqrt{4-\sqrt{15}}\)
\(\sqrt{2}.\left(\sqrt{8}-\sqrt{32}+3\sqrt{18}\right)\)
\(\sqrt{2}.\left(\sqrt{2}-\sqrt{3-\sqrt{5}}\right)\)
\(\sqrt{3}-\sqrt{2}.\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}\)
\(\left(\sqrt{2}-\sqrt{3+\sqrt{5}}\right).\sqrt{2}+2\sqrt{5}\)
2. Giai pt
\(\sqrt{4x^2-4x+1}=5\)
\(\sqrt{4x-12}+\frac{1}{3}.\sqrt{9x-27}=4+\sqrt{x-3}\)
\(\sqrt{4x+8}-\sqrt{9x+18}-2\sqrt{x+2}=21\)
\(\left(3-2\sqrt{x}\right).\left(2+3\sqrt{x}\right)=16-6x\)
\(\sqrt{x^2-4}-\sqrt{x-2}=0\)
Rút gọn biểu thức sau
A=\(\dfrac{1}{x-1}\sqrt{75\left(x-1\right)^3}\left(x>1\right)
\)
B=\(5\sqrt{4x}-3\sqrt{\dfrac{100x}{9}}-\dfrac{4}{x}\sqrt{\dfrac{x^3}{4}}\left(x>0\right)
\)
C=\(x-4+\sqrt{16-8x+x^2}\left(x>4\right)\)
Help me
\(\left(5\right)\sqrt{x+3-4\sqrt{x-1}}\sqrt{x+8+6\sqrt{x-1}}=5\)
\(\left(6\right)2x^2+3x+\sqrt{2x^2+3x+9}=33\)
\(\left(7\right)\sqrt{3x^2+6x+12}+\sqrt{5x^4-10x^2+30}=8\)
\(\left(8\right)x+y+z+8=2\sqrt{x-1}+4\sqrt{y-2}+6\sqrt{z-3}\)
