2ⁿ⁺³ + 2ⁿ⁺² - 2ⁿ⁺¹ + 2ⁿ = 2ⁿ.2³ + 2ⁿ.2² - 2ⁿ.2 + 2ⁿ

= 2ⁿ.(2³ + 2² - 2 + 1)

= 2ⁿ.11

sửa lại đề nè:

So sánh: 2⁹¹ và 5³⁵

Ta có: 2⁹¹ = (2¹³)⁷ = 8192⁷

5³⁵ = (5⁵)⁷ = 3125⁷

Vì 8192⁷>3125⁷

=> 2⁹¹>5³⁵

câu hỏi đâu ?

\(C=\frac{5x^2+3y^2}{10x^2-3y^2}\)

Có \(\frac{x}{3}=\frac{y}{5}\Rightarrow\frac{x}{y}=\frac{3}{5}\)

Thay \(x=3;y=5\) ta có : \(\frac{5x^2+3y^2}{10x^2-3y^2}=\frac{5\cdot3^2+3\cdot5^2}{10\cdot3^2-3\cdot5^2}=8\)

Vậy \(C=8\)

\(\left(x-3\right)^2+\left|y^2-9\right|=0\)

Vì \(\left\{{}\begin{matrix}\left(x-3\right)^2\ge0\forall x\\\left|y^2-9\right|\ge0\forall y\end{matrix}\right.\)

để bt = 0 \(\Leftrightarrow\left\{{}\begin{matrix}\left(x-3\right)^2=0\\\left|y^2-9\right|=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-3=0\\y^2-9=0\Rightarrow y^2=9\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=3\\\left[{}\begin{matrix}y=3\\y=-3\end{matrix}\right.\end{matrix}\right.\)

Vậy.....

\(\left(x-3\right)^2+\left|y^2-9\right|=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-3\right)^2=0\\\left|y^2-9\right|=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x-3=0\\y^2-9=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\y^2=9\left[{}\begin{matrix}y=3\\y=-3\end{matrix}\right.\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=3\\y=3hoặcy=-3\end{matrix}\right.\)

\(3x^2y^4\)-\(5xy^3\)-\(\dfrac{3}{2}x^2y^4\)+\(3xy^3\)+\(2xy^3\)+1=1,5\(x^2y^4\)+1>0

3x² y⁴ - 5xy³ -3/2 x2y⁴ + 3xy³ + 2xy³ +1

=\(\dfrac{3}{2}x^2y^4+1\)

Ta có:x²\(\ge0\forall x\in Q\)

y^{4\(\ge0\forall x\in Q\)}

\(\Rightarrow x^2y^4\)\(\ge0\forall x\in Q\)

\(\Rightarrow\dfrac{3}{2}\)\(x^2y^4\) \(\ge0\forall x\in Q\)

\(\Rightarrow\dfrac{3}{2}\)\(x^2y^4\) \(\ge1\forall x\in Q\) (đpcm)