<3,6km/h=1m/s>

36km/h=10m/s

108km/h=30m/s

15m/s=54km/h

20m/s=72km/h

12000m/h=\(\dfrac{10}{3}\)m/s

180m/min=3m/s

Ta có :

\(A=h\left(h+1\right)\left(h+2\right)\left(h+3\right)\)

\(=h\left(h+3\right)\left(h+1\right)\left(h+2\right)\)

\(=\left(h^2+3h\right)\left(h^2+3h+2\right)\)

\(=\left(h^2+3h+1-1\right)\left(h^2+3h+1+1\right)\)

\(=\left(h^2+3h+1\right)^2-1\)

Do : \(\left(h^2+3h+1\right)^2\ge0\Rightarrow\left(h^2+3h+1\right)^2-1\ge-1\)

Vậy \(MIN_A=-1\)

A = h( h + 1)( h + 2)( h + 3)

A = ( h² + 3h)( h² + 3h + 2)

Đặt : h² + 3h + 1 = a , ta có :

A = ( a - 1)( a + 1)

A = a² - 1

Thay : h² + 3h + 1 = a , ta có :

A = ( h² + 3h + 1 )² - 1

=> A_min = -1 khi : ( h + \(\dfrac{3}{2}\))² - \(\dfrac{5}{4}\) = 0 <=> h + \(\dfrac{3}{2}\) = \(\dfrac{\sqrt{5}}{2}\) <=>h= \(\dfrac{\sqrt{5}-3}{2}\)

\(-1\le sinx\le1\Rightarrow-3\le-3sinx\le3\)

\(\Rightarrow1\le4-3sinx\le7\)

\(\Rightarrow4\le y\le10\)

\(\Rightarrow y_{max}=10\) khi \(sinx=-1\)

\(y_{min}=4\) khi \(sinx=1\)

Vì 3 ≤ x ≤ 7 => x - 3 ≥ 0; 7 - x ≥ 0

=> C ≥ 0

Dấu = xảy ra khi và chỉ khi x = 3 hoặc x = 7

C = (x - 3)(7 - x) ≤ \(\dfrac{1}{4}\)(x - 3 + 7 - x)² = \(\dfrac{1}{4}\).4² = 4

Dấu "=" xảy ra <=> x - 3 = 7 - x <=> x = 5

\(G=\left(x^2+\sqrt[3]{3}\right)+\left(\dfrac{2}{x^3}+\dfrac{2}{\sqrt{3}}+\dfrac{2}{\sqrt{3}}\right)-\sqrt[3]{3}-\dfrac{4}{\sqrt{3}}\ge2\sqrt{x^2.\sqrt[3]{3}}+3\sqrt[3]{\dfrac{2}{x^3}.\dfrac{2}{\sqrt{3}}.\dfrac{2}{\sqrt{3}}}-\sqrt[3]{3}-\dfrac{4}{\sqrt{3}}=2\sqrt[6]{3}.x+\dfrac{6}{\sqrt[3]{3}x}-\sqrt[3]{3}-\dfrac{4}{\sqrt{3}}\ge2\sqrt{2\sqrt[6]{3}.x.\dfrac{6}{\sqrt[3]{3}x}}-\sqrt[3]{3}-\dfrac{4}{\sqrt{3}}=2\sqrt{\dfrac{12\sqrt[6]{3}}{\sqrt[3]{3}}}-\sqrt[3]{3}-\dfrac{4}{\sqrt{3}}\)

Dấu "=" xảy ra khi và chỉ khi \(x=\sqrt[6]{3}\)

Cô - si cho 5 số lên mạng search cách chứng minh nhé

\(G=\dfrac{1}{3}x^2+\dfrac{1}{3}x^2+\dfrac{1}{3}x^2+\dfrac{1}{x^3}+\dfrac{1}{x^3}\ge5\sqrt[5]{\dfrac{1}{3^3}.\dfrac{x^2.x^2.x^2}{x^3.x^3}}=5\sqrt[5]{\dfrac{1}{27}}\)

Dấu "=" xảy ra <=> \(\dfrac{1}{3}x^2=x^3\)

<=> \(x^5=3\)

<=> \(x=\sqrt[5]{3}\)