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Bài 3:
c: Ta có: \(3x-5-5\sqrt{x-1}=0\)
\(\Leftrightarrow5\sqrt{x-1}=3x-5\)
\(\Leftrightarrow25x-25=9x^2-30x+25\)
\(\Leftrightarrow9x^2-55x+50=0\)
\(\text{Δ}=\left(-55\right)^2-4\cdot9\cdot50=1225\)
Vì Δ>0 nên phương trình có hai nghiệm phân biệt là:
\(\left\{{}\begin{matrix}x_1=\dfrac{55-35}{18}=\dfrac{10}{9}\\x_2=\dfrac{55+35}{18}=5\end{matrix}\right.\)
\(\text{8.C.So le trong}\)
\(\text{9.C.a trùng b}\)
\(\text{10.B.}60^0\)
\(\text{11.C.}150^0\)
\(\text{12.B.A=P}\)
1 do you do
2 had done - went
3 went - had read
4 will attend
5 hadn't worn
6 to be
7 weren't sleeping - were playing
8 to be
9 had lived - moved
10 locking
11 had work - retired
12 told - had learned
13 won't call
14 had met
do you do
had done-went
went- had read
will attend
hadn't worn
to be
\(\dfrac{x}{27}=\dfrac{2}{9}-\dfrac{1}{3}\Rightarrow\dfrac{x}{27}=-\dfrac{1}{9}\Rightarrow\dfrac{x}{27}=\dfrac{-3}{27}\Rightarrow x=27\)
\(\dfrac{x}{27}=\dfrac{2}{9}-\dfrac{1}{3}=-\dfrac{1}{9}\Rightarrow x=-\dfrac{1}{9}.27=-3\).
1 were - would you play
2 weren't studying - would have
3 had taken - wouldn't have got
4 would you go - could
5 will you give - is
6 recycle - won't be
7 had heard - wouldn't have gone
8 would you buy - had
9 don't hurry - will miss
10 had phoned - would have given
11 were - wouldn't eat
12 will go - rains
13 had known - would have sent
14 won't feel - swims
15 hadn't freezed - would have gone
a: Xét tứ giác AEHF có
\(\widehat{AEH}=\widehat{AFH}=\widehat{FAE}=90^0\)
Do đó: AEHF là hình chữ nhật
24 B
25 B
26 C
27 B
28 C
29 C
30 C
31 A
32 B
33 C
34 A
35 B
36 B
37 C
38 B
39 C
Bài 2:
a) Ta có: \(\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}+\dfrac{6}{2-\sqrt{10}}-\dfrac{20}{\sqrt{10}}\)
\(=\dfrac{\sqrt{10}\left(\sqrt{5}-\sqrt{2}\right)}{\sqrt{5}-\sqrt{2}}+\dfrac{6\cdot\left(\sqrt{10}+2\right)}{\left(\sqrt{10}-2\right)\left(\sqrt{10}+2\right)}-\dfrac{\sqrt{10}\cdot2\sqrt{10}}{\sqrt{10}}\)
\(=\sqrt{10}+\sqrt{10}-2-2\sqrt{10}\)
=-2
b) Ta có: \(\left(\dfrac{5-\sqrt{5}}{\sqrt{5}}-2\right)\left(\dfrac{4}{1+\sqrt{5}}+4\right)\)
\(=\left(\sqrt{5}-1-2\right)\left(\sqrt{5}-1+4\right)\)
\(=\left(\sqrt{5}-3\right)\left(\sqrt{5}+3\right)\)
=5-9=-4
c) Ta có: \(\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\dfrac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\dfrac{\sqrt{5}+1}{\sqrt{5}-1}\)
\(=\dfrac{\left(\sqrt{5}-\sqrt{3}\right)^2+\left(\sqrt{5}+\sqrt{3}\right)^2}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}-\dfrac{\left(\sqrt{5}+1\right)^2}{\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)}\)
\(=\dfrac{8-2\sqrt{15}+8+2\sqrt{15}}{2}-\dfrac{6+2\sqrt{5}}{4}\)
\(=\dfrac{16}{2}-\dfrac{6+2\sqrt{5}}{4}\)
\(=\dfrac{32-6-2\sqrt{5}}{4}\)
\(=\dfrac{26-2\sqrt{5}}{4}\)
\(=\dfrac{13-\sqrt{5}}{2}\)