\(\sqrt{31-12\sqrt{3}}+\sqrt{31+12\sqrt{3}}\)
=\(\sqrt{\left(3\sqrt{3}\right)^2-2.3\sqrt{3}.2+4}+\sqrt{\left(3\sqrt{3}\right)^2+2.3\sqrt{3}.2+4}\)
=\(\sqrt{\left(3\sqrt{3}-2\right)^2}+\sqrt{\left(3\sqrt{3}+2\right)^2}\)
=\(3\sqrt{3}-2+3\sqrt{3}+2=6\sqrt{3}\)
P=\(\left(\frac{3}{\sqrt{a+2}}+\sqrt{a+2}\right):\left(2+\frac{6}{\sqrt{a^2-4}}\right)\)
a) Rút gọn biểu thức P
b) Tính giá trị biểu thức tại \(a=31-12\sqrt{5}\)
a) A=\(\sqrt{\left(4-\sqrt{15}\right)^2+\sqrt{15}}\)
b) B=\(\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{\left(1-\sqrt{3}\right)^2}\)
c) C=\(\sqrt{49-12\sqrt{5}}-\sqrt{49+12\sqrt{5}}\)
d)D=\(\sqrt{29+12\sqrt{5}-\sqrt{29-12\sqrt{5}}}\)
Tìm x để các căn bậc hai sau có nghĩa
a) \(\sqrt{\dfrac{15+3x^2}{-6}}\) b) \(\sqrt{\dfrac{-81}{-12-x^2}}\)
c) \(\sqrt{\dfrac{31\left(x^2+21\right)}{3}}\) d) \(\sqrt{\dfrac{-12}{11+x^2}}\)
e) \(\sqrt{\dfrac{21}{-x^2-17}}\)
Mọi người cho em hỏi:
\(\left(\frac{\sqrt{x}}{\left[\sqrt{x}-3\right]\left[\sqrt{x}+3\right]}+\frac{2}{\sqrt{x}+3}-\frac{3}{\sqrt{x}-3}\right):\left(\sqrt{x}-3+\frac{12-x}{\sqrt{x}+3}\right)\)
\(\left(\frac{\sqrt{x}+2\left[\sqrt{x}-3\right]-3\left[\sqrt{x}+3\right]}{\left[\sqrt{x}-3\right]\left[\sqrt{x}+3\right]}\right):\left(\frac{\left[\sqrt{x}-3\right]\left[\sqrt{x}+3\right]+12-x}{\sqrt{x}-3}\right)\)
\(\left(\frac{\sqrt{x}+2\sqrt{x}-6-3\sqrt{x}-9}{\left[\sqrt{x}+3\right]\left[\sqrt{x}-3\right]}\right):\left(\frac{x+3\sqrt{x}-3\sqrt{x}-9+12-x}{\sqrt{x}+3}\right)\)
\(\left(\frac{-15}{\left[\sqrt{x}+3\right]\left[\sqrt{x}-3\right]}\right):\left(\frac{3}{\sqrt{x}+3}\right)\)
\(\left(\frac{-15}{\left[\sqrt{x}+3\right]\left[\sqrt{x}-3\right]}\right).\left(\frac{\sqrt{x}+3}{3}\right)\)
\(\frac{-5}{\sqrt{x}-3}\)
31 A=\(\left(\dfrac{x-5\sqrt{x}}{x-25}-1\right):\left(\dfrac{25-x}{x+2\sqrt{x}-15}-\dfrac{\sqrt{x}+3}{\sqrt{x}+5}+\dfrac{\sqrt{x}-5}{\sqrt{x}+3}\right)\)
a. rút gọn
b. tính A với x thỏa mãn \(x-5\sqrt{x}+6=0\)
thực hiện phép tính
\(\sqrt{\left(4-\sqrt{5}\right)^2}+\sqrt{5+2\sqrt{5}+1}\)
giải phương trình
\(\sqrt{x-3}=6\)
\(\sqrt{\left(x-3\right)^2}=12\)
rút gọn biểu thức
a) \(P=\left(\dfrac{3-x\sqrt{x}}{3-\sqrt{x}}+\sqrt{x}\right).\left(\dfrac{3-\sqrt{x}}{3-x}\right)\) (với x≥0 ; x≠3; x≠9
b) \(P=\left(\dfrac{1}{\sqrt{x}+1}-\dfrac{1}{x+\sqrt{x}}\right)\div\dfrac{x-\sqrt{x}+1}{x\sqrt{x}+1}\) (x >0)
c) \(A=\sqrt{3x-1}+3.\sqrt{12x-4}-\sqrt{6^2.\left(3x-1\right)}+\sqrt{5}\) với x≥ \(\dfrac{1}{3}\)
d) \(A=\left(\dfrac{a\sqrt{a}-1}{a-\sqrt{a}}-\dfrac{a\sqrt{a}+1}{a+\sqrt{a}}\right):\dfrac{a+2}{a-2}\) với a>0,a≠1, a≠ \(\pm\)2
Tính giá trị M=\(\left(x-y\right)^3+3\left(x-y\right)\left(xy+1\right)\)biết x=\(\sqrt[3]{3+2\sqrt{2}}+\sqrt[3]{3-2\sqrt{2}}\)
y=\(\sqrt[3]{17+12\sqrt{2}}-\sqrt[3]{17-12\sqrt{2}}\)
Tính:
\(\left(3\sqrt{18}-2\sqrt{17}-\sqrt{45}\right):\left(3\sqrt{8}+\sqrt{20}-2\sqrt{12}\right)\)
cho hàm số
\(f\left(x\right)=\left(x^3+12x-31\right)^{2012}\)
tính \(f\left(a\right)\)tại \(a=\sqrt[3]{16-8\sqrt{5}}+\sqrt[3]{16+8\sqrt{5}}\)
