5(x - 35) - 75 = 475

=> 5x - 175 = 550

=> 5x = 725

=> x = 145

vậy)

5 . ( x - 35 ) - 75 = 475

5 . ( x - 35 ) = 475 - 75 

5 . ( x - 35 ) = 400

x - 35 = 400 : 5

x - 35 = 80

 x = 80 + 35 

x = 115

Vậy x = 115

Vì a,b > 0 nên \(\frac{a+b}{\sqrt{a^2+4}}\le\sqrt{\frac{3}{2}}\Leftrightarrow\frac{\left(a+b\right)^2}{a^2+4}\le\frac{3}{2}\Leftrightarrow\frac{\left(a+b\right)^2}{2a^2+b^2}\le\frac{3}{2}\)

\(\Leftrightarrow\frac{\left(a+b\right)^2}{2a^2+b^2}-\frac{3}{2}\le0\Leftrightarrow\frac{2a^2+4ab+2b^2-6a^2-3b^2}{2\left(2a^2+b^2\right)}\le0\)

\(\Leftrightarrow\frac{-4a^2+4ab-b^2}{2\left(2a^2+b^2\right)}\le0\Leftrightarrow\frac{-\left(2a-b\right)^2}{2\left(2a^2+b^2\right)}\le0\)(Đúng)

Đẳng thức xảy ra khi \(\hept{\begin{cases}a^2+b^2=4\\2a-b=0\end{cases}}\Leftrightarrow\hept{\begin{cases}a=\frac{2}{\sqrt{5}}\\b=\frac{4}{\sqrt{5}}\end{cases}}\)

Hướng dẫn:

Ta có \(\left(a+b\right)^2=\left(\sqrt{2}a\cdot\frac{1}{\sqrt{2}}+b\cdot1\right)^2\le\left(2a^2+b^2\right)\cdot\left(\frac{1}{2}+1\right)\)

\(\Rightarrow\left(a+b\right)^2\le\left(a^2+4\right)\cdot\frac{3}{2}\)

\(\Rightarrow\frac{a+b}{\sqrt{a^2+4}}\le\sqrt{\frac{3}{2}}\)

a, 3x^2 - 15 = 93

=> 3x^2 = 108

=> x^2 = 36

=> x = 6 hoặc x = -6

b, 12x - 72 = 2^2.3^3

=> 12x - 72 = 108

=> 12x = 180

=> x = 15 

c, (5x - 2)^3 = 27

=> 5x - 2 = 3

=> 5x = 5

=> x = 1

d, (7x - 1)(3x - 12) = 0

=> (7x - 1)3(x - 4) = 0

=> 7x - 1 = 0 hoặc x - 4 = 0

=> x = 1/7 hoặc x = 4

a, \(3x^2-15=93\)

\(\Rightarrow3x^2=108\)

\(\Rightarrow x^2=36\)

\(\Rightarrow\orbr{\begin{cases}x=6\\x=-6\end{cases}}\)

b,\(12x-72=2^2\times3^3\)

\(\Rightarrow12x-72=108\)

\(\Rightarrow12x=180\)

\(\Rightarrow x=15\)

c,\(\left(5x-2\right)^3=27\)

\(\Rightarrow\left(5x-2\right)^3=3^3\)

\(\Rightarrow5x-2=3\)

\(\Rightarrow5x=5\)

\(\Rightarrow x=1\)

d,\(\left(7x-1\right)\left(3x-12\right)=0\)

\(\Rightarrow\orbr{\begin{cases}7x-1=0\\3x-12=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}7x=1\\3x=12\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{1}{7}\\x=4\end{cases}}\)

~Std well~

\(\left(x+y\right)^2+\frac{x+y}{2}=\left(x+y\right)\left(x+\frac{1}{4}+y+\frac{1}{4}\right)\ge2\sqrt{xy}\left(\sqrt{x}+\sqrt{y}\right)\ge2x\sqrt{y}+2y\sqrt{x}\)

Dau '=' xay ra khi \(x=y=\frac{1}{4}\)

1235642 × 88 ÷ 88 - 123333

= 1235642 - 123333

= 1112309

~Std well~

1+1=2 

nha

bn

k

cho

mk

nha

Trả lời :

= 2

#Cbht nha cauu

11111 : 11111

a ) [ 540 - ( 45 + 4 x 25 ) ] : 50 - 2000 : 250 + 2¹⁵ : 2¹³

= [540 - (45 + 100)] : 50 - 8 + 2²

= [540 - 145] : 50 - 8 + 4

= 395 : 50 - 4

= 7,9 - 4

= 3,9

[540 - (45 + 4 x 25)] : 50 - 2000 : 250 + 2¹⁵ : 2¹³

= [540 - (45 + 100)] : 50 - 8 + 2^{15 - 13}

= [540 - 145] : 50 - 8 + 2²

= 395 : 50 - 8 + 4

= 7,9 - 8 + 4

 = 3,9