20 - 6 = ?
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\(M=\dfrac{40^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}\)
\(=\dfrac{\left(2^3.5\right)^{20}-2^{20}+\left(2.3\right)^{20}}{\left(2.3\right)^{20}-3^{20}+\left(3^2\right)^{20}}\)
\(=\dfrac{2^{60}.5^{20}-2^{20}+2^{20}.3^{20}}{2^{20}.3^{20}-3^{20}+3^{20}}\)
\(=\dfrac{2^{20}\left(2^{30}.5^{20}-1+3^{20}\right)}{3^{20}\left(2^{20}-1+3^{20}\right)}\)
có nhầm đề k nhỉ ?
a. \(\sqrt{49-20\sqrt{6}}-\sqrt{106+20\sqrt{6}}=\sqrt{\left(5-2\sqrt{6}\right)^2}-\sqrt{\left(10+\sqrt{6}\right)^2}=5-2\sqrt{6}-10-\sqrt{6}=-5-3\sqrt{6}\)
b. \(\sqrt{83-20\sqrt{6}}+\sqrt{62-20\sqrt{6}}=\sqrt{\left(5\sqrt{3}-2\sqrt{2}\right)^2}+\sqrt{\left(5\sqrt{2}-2\sqrt{3}\right)^2}=5\sqrt{3}-2\sqrt{2}+5\sqrt{2}-2\sqrt{3}=3\sqrt{3}+3\sqrt{2}\)
c. \(\sqrt{302-20\sqrt{6}}+\sqrt{203-20\sqrt{6}}=\sqrt{\left(10\sqrt{3}-\sqrt{2}\right)^2}+\sqrt{\left(10\sqrt{2}-\sqrt{3}\right)^2}=10\sqrt{3}-\sqrt{2}+10\sqrt{2}-\sqrt{3}=9\sqrt{3}+9\sqrt{2}\)
d. \(\sqrt{601-20\sqrt{6}}-\sqrt{154-20\sqrt{6}}=\sqrt{\left(10\sqrt{6}-1\right)^2}-\sqrt{\left(5\sqrt{6}-2\right)^2}=10\sqrt{6}-1-5\sqrt{6}+2=1+5\sqrt{6}\)
\(\frac{4^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}=\frac{\left(2^2\right)^{20}-2^{20}+\left(3.2\right)^{20}}{\left(3.2\right)^{20}-3^{20}+\left(3^2\right)^{20}}=\frac{2^{20}.2^{20}-2^{20}.1+3^{20}.2^{20}}{3^{20}.2^{20}-3^{20}.1+3^{20}.3^{20}}=\frac{2^{20}.\left(2^{20}-1+3^{20}\right)}{3^{20}.\left(2^{20}-1+3^{20}\right)}=\frac{2^{20}}{3^{20}}=\left(\frac{2}{3}\right)^{20}=\frac{40}{60}=\frac{2}{3}\)
20-6=14
chúc bạn học giỏi
khoan lớp 1 mà đã nhớ rồi hả?
\(14\)