\(a)\)

Cách 1 : 

\(2^{30}+3^{30}+4^{30}\ge3\sqrt[3]{\left(2.3.4\right)^{30}}=3.\left(2.3.4\right)^{10}=3.24^{10}\) ( Cosi ) 

Mà \(2^{30}\ne3^{30}\ne4^{30}\) nên dấu "=" không xảy ra hay \(2^{30}+3^{30}+4^{30}>3.24^{10}\)

Vậy ... 

Cách 2 : 

\(4^{30}=4^{11}.4^{19}=4^{11}.2^{38}>3^{11}.2^{30}=3.3^{10}.8^{10}=3.24^{10}\)

Vậy ... 

\(b)\)\(4+\sqrt{33}=\sqrt{16}+\sqrt{33}>\sqrt{14}+\sqrt{29}\)

Vậy ... 

Tính từ máy tính casio fx 570 es plus hoặc fx 570 vn plus

Ta thu đc kết quả:

A>B

Ta có :

1) 45^10 . 5^30= (5.9)^10 . 5^30 = 5^10 . 5^30 . 9^10 = 5^40 . 3^20 = 25^20 . 3^20=75^20

2)\(\sqrt{40+2}=\sqrt{42}<\sqrt{49}=7=6+1=\sqrt{36}+\sqrt{1}<\sqrt{40}+\sqrt{2}\)

Vậy \(\sqrt{40+2}<\sqrt{40}+\sqrt{2}\)

3)\(Cho\frac{x}{3}=\frac{y}{4}=k\Rightarrow x=3k;y=4k\)

Ta lại có:

\(xy=12\Rightarrow3k.4k=12\)

\(12.k^2=12\Rightarrow k^2=1\Rightarrow k=1:-1\)

\(Vơik=1\Rightarrow x=1.3=3;y=1.4=4\)

\(k=-1\Rightarrow x=-1.3=-3;y=-1.4=-4\)

a) Ta có: \(99^{20}=\left(99^2\right)^{10}=9801^{10}< 9999^{10}\Rightarrow99^{20}< 9999^{10}\)

b) Ta có: \(2^{31}=\left(2\frac{31}{21}\right)^{21}=2,7822^{21}< 3^{21}\Rightarrow2^{31}< 3^{21}\)

c) Ta có: \(3^{30}=\left(3^3\right)^{10}=27^{10}\)

\(2^{30}=\left(2^3\right)^{10}=8^{10}\)

\(4^{30}=\left(4^3\right)^{10}=64^{10}\)

Lại có: \(3.24^{10}=2.24^{10}+24^{10}\Rightarrow24^{10}< 27^{10}\left(1\right)\)

\(2.24^{10}< 48^{10}< 64^{10}\left(2\right)\)

Từ 1,2 => \(24^{10}+2.24^{10}< 27^{10}+64^{10}\Rightarrow3.24^{10}< 8^{10}+27^{10}+64^{10}\)

\(\Rightarrow3.24^{10}< 3^{30}+2^{30}+4^{30}\)

4^30=2^30*2^30

=2^30*4^15

3*24^10=3*3^10*8^10=3^11*2^30

mà 4^30>3^11

nên 2^30+3^30+4^30>3*24^10

a) S=1+5²+5⁴+.....+5²⁰⁰

=>5²S=25S=5²+5⁴+5⁶+.....+5²⁰²

=>25S-S=(5²+5⁴+5⁶+....+5²⁰²)-(1+5²+5⁴+......+5²⁰⁰)

=>24S=5²⁰²-1

=>S=\(\frac{5^{202}-1}{24}\)

a) lấy 5S-S

b)trên olm có