1 .......... good that I have watched it 3 times

2 .......... it rained heavily, we didn't get wet as we got home

4 I admire the girl who didn't hesitate to save the kids from the crazy bus

5 ......... am excited about seeing you this weekend

\(f\left(1\right)=a\cdot1^2+b\cdot1+c\)

=a+b+c

\(f\left(-3\right)=a\cdot\left(-3\right)^2+b\cdot\left(-3\right)+c\)

=9a-3b+c

3*f(1)=3a+3b+3c; 2f(-3)=18a-6b+2c

3f(1)+2f(-3)=3a+3b+3c+18a-6b+2c=21a-3b+5c=0

=>3f(1)=-2f(-3)

=>f(1)=-2/3*f(-3)

=>\(f\left(1\right)\cdot f\left(-3\right)=-\frac23\cdot f^2\left(-3\right)\le0\) (ĐPCM)

\(\Leftrightarrow a\sqrt{a}+b\sqrt{b}\ge\left(\sqrt{a}+\sqrt{b}\right)^2\)

\(\Leftrightarrow\left(\sqrt{a}+\sqrt{b}\right)\left(a-\sqrt{ab}+b-\sqrt{a}-\sqrt{b}\right)>=0\)(đúng)

Đặt \(cosx-sinx=t\Rightarrow-\sqrt{2}\le t\le\sqrt{2}\)

\(t^2=1-2sinx.cosx\Rightarrow sinx.cosx=\dfrac{1-t^2}{2}\)

Pt trở thành:

\(t\left(1+\dfrac{1-t^2}{2}\right)+1=0\)

\(\Leftrightarrow t^3-3t-2=0\)

\(\Leftrightarrow\left(t-2\right)\left(t+1\right)^2=0\Rightarrow\left[{}\begin{matrix}t=2\left(loại\right)\\t=-1\end{matrix}\right.\)

\(\Rightarrow cosx-sinx=-1\)

\(\Leftrightarrow\sqrt[]{2}cos\left(x+\dfrac{\pi}{4}\right)=-1\)

\(\Leftrightarrow cos\left(x+\dfrac{\pi}{4}\right)=-\dfrac{\sqrt{2}}{2}\)

\(\Leftrightarrow cos\left(x+\dfrac{\pi}{4}\right)=cos\left(\dfrac{3\pi}{4}\right)\)

\(\Leftrightarrow...\)

tìm minx max của biểu thức ạ

a)2 + 5 + 11 + ... + 47+ 95
Tính chất : 5 = 2.2 + 1
11 = 5.2 + 1
Vậy các số của dãy là: 2 + 5 + 7 + 11 + 23 + 47 + 95
= (2 + 5 + 7) + (5 + 95) + (23 + 47)
= 14 + 100 + 70
= 184

(27 + 29) + (86 - 84) + 5

= 56 + 2 + 5

= 63

Chúc bạn học tốt!! ^^

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