Sao lại có chữ "`2` điểm" nhỉ ._.?

16h52p

6 ngày 8h

29h32p

4p19s

a) \(\dfrac{5+\sqrt{5}}{5-\sqrt{5}}+\dfrac{5-\sqrt{5}}{5+\sqrt{5}}=\dfrac{\sqrt{5}\left(\sqrt{5}+1\right)}{\sqrt{5}\left(\sqrt{5}-1\right)}+\dfrac{\sqrt{5}\left(\sqrt{5}-1\right)}{\sqrt{5}\left(\sqrt{5}+1\right)}\)

\(=\dfrac{\sqrt{5}+1}{\sqrt{5}-1}+\dfrac{\sqrt{5}-1}{\sqrt{5}+1}=\dfrac{\left(\sqrt{5}+1\right)^2+\left(\sqrt{5}-1\right)^2}{\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)}=\dfrac{12}{4}=3\)

b) \(\dfrac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}=\dfrac{-\sqrt{2}\left(\sqrt{6}-4\right)}{\sqrt{3}\left(\sqrt{6}-4\right)}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{6}\left(\sqrt{5}+\sqrt{27}\right)}\)

\(=\dfrac{-\sqrt{2}}{\sqrt{3}}-\dfrac{1}{\sqrt{6}}=\dfrac{-3}{\sqrt{6}}=\dfrac{-\sqrt{3}}{\sqrt{2}}\)

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

\(=9+4\sqrt{5}-3=6+4\sqrt{5}\)

d) \(\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}}+\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}}\)

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

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

c) \(\dfrac{2\sqrt{10}+\sqrt{30}-2\sqrt{2}-\sqrt{6}}{2\sqrt{10}-2\sqrt{2}}=1+\dfrac{\sqrt{30}-\sqrt{6}}{2\sqrt{10}-2\sqrt{2}}=1+\dfrac{\sqrt{6}\left(\sqrt{5}-1\right)}{2\sqrt{2}\left(\sqrt{5}-1\right)}\)

\(=1+\dfrac{\sqrt{6}}{2\sqrt{2}}=1+\dfrac{\sqrt{3}}{2}=\dfrac{2+\sqrt{3}}{2}\)

d) \(\sqrt{\left(1-\sqrt{2016}\right)^2}.\sqrt{2017+2\sqrt{2016}}=\left|1-\sqrt{2016}\right|\sqrt{\left(\sqrt{2016}+1\right)^2}\)

\(=\left(\sqrt{2016}+1\right)\left(\sqrt{2016}-1\right)=2015\)

e) \(\left(\sqrt{15}+2\sqrt{3}\right)^2+12\sqrt{5}=27+12\sqrt{5}+12\sqrt{5}=27+24\sqrt{5}\)

f) \(2\sqrt{5}\left(2-3\sqrt{5}\right)+\left(1-2\sqrt{5}\right)^2+6\sqrt{5}\)

\(=4\sqrt{5}-30+21-4\sqrt{5}+6\sqrt{5}=6\sqrt{5}-9\)

\(2\sqrt{5}\left(2-3\sqrt{5}\right)+\left(1-2\sqrt{5}\right)^2+6\sqrt{5}=4\sqrt{5}-30+20+1-4\sqrt{5}+6\sqrt{5}\)

\(=6\sqrt{5}-9\)

Olm chào em, bài này thì em làm như sau em nhé:

                              

Gọi B là góc tạo bởi tia nắng với mặt đất, AC chiều cao tháp, AB là bóng của tháp

Áp dụng tslg trong tam giác ABC vuông tại A:

\(tanB=\dfrac{AC}{AB}\Rightarrow AC=100.tan40^0\approx84\left(m\right)\)

= 50

50

(100^23:100^20).20

= (1000000000000000000000000 : 100000000000000000000)x20

= 10000x20

=200000.

cảm ơn bạn nha

686,7

686,7

Câu này chỉ có tính máy:

12345678987654321.11 = 1.358024689x10¹⁷

sai rồi anh ơi