Ta có

•   A=1+3⁴+3⁸+3¹²

=>3⁴.A=3⁴+3⁸+3¹²+3¹⁶

<=>81.A-A=3¹⁶-1

<=>A=(3¹⁶-1)/80=538084

•B=1+3²+3⁴+3⁶+3⁸+3¹⁰+3¹²+3¹⁴

=>3².B=3²+3⁴+3⁶+3⁸+3¹⁰+3¹²+3¹⁴+3¹⁶

<=>8.B=3¹⁶-1

<=>B=(3¹⁶-1)/8=53808400

Vậy Q=A/B=538084/53808400=1/100=0.01

Sửa lại:

B=5380840

=>Q=1/10

\(Q=\frac{1+3^4+3^8+3^{12}}{\left(1+3^4+3^8+3^{12}\right)+3^2\left(1+3^4+3^8+3^{12}\right)}\)

\(Q=\frac{1+3^4+3^8+3^{12}}{10\left(1+3^4+3^8+3^{12}\right)}=\frac{1}{10}\)

Cj ko rep đc kịp sr nha

a: \(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)

\(=\sqrt{9-2\cdot3\cdot\sqrt{6}+6}+\sqrt{24-2\cdot2\sqrt{6}\cdot3+9}\)

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

\(=3-\sqrt{6}+2\sqrt{6}-3=\sqrt{6}\)

b: \(\sqrt{\left(3+\sqrt{5}\right)^2}+\sqrt{14-6\sqrt{5}}\)

\(=\sqrt{\left(3+\sqrt{5}\right)^2}+\sqrt{\left(3-\sqrt{5}\right)^2}\)

\(=\left|3+\sqrt{5}\right|+\left|3-\sqrt{5}\right|\)

\(=3+\sqrt{5}+3-\sqrt{5}=6\)

c: \(\dfrac{3}{2\sqrt{3}+3}+\dfrac{3}{2\sqrt{3}-3}\)

\(=\dfrac{3\left(2\sqrt{3}-3\right)+3\left(2\sqrt{3}+3\right)}{12-9}\)

\(=2\sqrt{3}-3+2\sqrt{3}+3=4\sqrt{3}\)

d: \(\sqrt{\left(\sqrt{3}+4\right)\cdot\sqrt{19-8\sqrt{3}}+3}\)

\(=\sqrt{\left(4+\sqrt{3}\right)\cdot\sqrt{\left(4-\sqrt{3}\right)^2}+3}\)

\(=\sqrt{\left(4+\sqrt{3}\right)\cdot\left(4-\sqrt{3}\right)+3}\)

\(=\sqrt{16-3+3}=\sqrt{16}=4\)

e: \(\dfrac{9-2\sqrt{3}}{3\sqrt{6}-2\sqrt{2}}+\dfrac{3}{3+\sqrt{6}}\)

\(=\dfrac{\sqrt{3}\left(3\sqrt{3}-2\right)}{\sqrt{2}\left(3\sqrt{3}-2\right)}+\dfrac{3\left(3-\sqrt{6}\right)}{3}\)

\(=\dfrac{\sqrt{6}}{2}+3-\sqrt{6}=3-\dfrac{\sqrt{6}}{2}\)

mẫu số :

(1+3^4+3^8+3^12)(1+9)=

ds=1/10

\(\frac{4^{10}+8^4}{4^5+8^6}=\frac{\left(2^2\right)^{10}+\left(2^3\right)^4}{\left(2^2\right)^5+\left(2^3\right)^6}=\frac{2^{2.10}+2^{3.4}}{2^{2.5}+2^{3.6}}=\)

\(=\frac{2^{20}+2^{12}}{2^{10}+2^{18}}\)

\(\frac{4^{10}+8^4}{4^5+8^6}=\frac{2^{20}+2^{12}}{2^{10}+2^{18}}=\frac{2^{12}.2^8+2^{12}}{2^{10}+2^{10}.2^8}=\frac{2^{12}\left(1+2^8\right)}{2^{10}\left(1+2^8\right)}=\frac{2^{12}}{2^{10}}=2^2=4\)