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\(\left(x-9\right)^3.\left(x^2-4\right)-x^2=-4\)
Đầu bài thế này hả bạn??
a)\(\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}=\frac{\left(2^2\right)^5.\left(3^2\right)^4-2.\left(2.3\right)^9}{2^{10}.3^8+\left(3.2\right)^8.2^2.5}=\frac{2^{10}.3^8-2.2^9.3^9}{2^{10}.3^8+3^8.2^8.2^2.5}=\frac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+3^8.2^{10}.5}\)
\(=\frac{2^{10}.3^8.\left(1-3\right)}{2^{10}.3^8.\left(1+5\right)}=\frac{-2}{6}=\frac{-1}{3}\)
b) đặt A=2100 - 299 + 298 - 297 +...+ 22 - 2
=>2A=2101-2100+299-298+...+23-22
=>2A+A=2101-2100+299-298+...+23-22+2100 - 299 + 298 - 297 +...+ 22 - 2
=>3A=2101-2
=>A=\(\frac{2^{101}-2}{3}\)
\(1,\\ a,\Rightarrow x=\dfrac{5\cdot4}{3}=\dfrac{20}{3}\\ b,\Rightarrow x=8\\ c,\Rightarrow x=\dfrac{27\cdot2}{3,6}=15\\ 2,\\ a,\dfrac{6}{9}=\dfrac{42}{63};\dfrac{6}{42}=\dfrac{9}{63};\dfrac{63}{9}=\dfrac{42}{6};\dfrac{63}{42}=\dfrac{9}{6}\\ b,\dfrac{4}{18}=\dfrac{2}{9};\dfrac{4}{2}=\dfrac{18}{9};\dfrac{9}{18}=\dfrac{2}{4};\dfrac{9}{2}=\dfrac{18}{4}\)
Đặt A = 2 . 3 + 3 . 4 + 4 . 5 + ... + 99 . 100
\(\Rightarrow\) 3A = 2 . 3 . (4 - 1) + 3 . 4 . (5 - 2) + 4 . 5 . (6 - 3) + ... + 99 . 100 . (101 - 98)
= 2 . 3 . 4 - 2 . 3 . 1 + 3 . 4 . 5 - 3 . 4 . 2 + 4 . 5 . 6 - 4 . 5 . 3 + ... + 99 . 100 . 101 - 99 . 100 . 98
= 6 + 999900 = 999906
\(\Rightarrow\) A = 333302