5.(x-35)-75=475
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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~
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
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