|x|+4x=6
(x+4)=y(x+1)
\(\left(x-5\right)\frac{30}{100}=\frac{20x}{100}+5\)
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\(\left(x-5\right).\frac{30}{100}=\frac{20x}{100}+5\)
\(\Leftrightarrow\left(x-5\right).0,3=0,2.x+5\)
\(\Leftrightarrow0,3.x-1,5=0,2.x+5\)
\(\Leftrightarrow0,3.x-0,2.x=5+1,5\)
\(\Leftrightarrow0,1.x=6,5\)
\(\Leftrightarrow x=65\)
\(\frac{\left(x-5\right).30}{100}=\frac{20x}{100}+\frac{500}{100}\)
\(\frac{30x-150}{100}=\frac{20x+500}{100}\)
=> 30x - 150 = 20x + 500
30x - 20x = 500 + 150
10x = 650
x = 65
Ta có: \(\left(x-5\right)\frac{30}{100}=\frac{20x}{100}+5\)
\(\Rightarrow\left(x-5\right)\frac{3}{10}=\frac{x}{5}+5\)
\(\Rightarrow\frac{3x-15}{10}=\frac{25+x}{5}\)
\(\Rightarrow5\left(3x-15\right)=10\left(25+x\right)\)
\(\Rightarrow15x-75=250+10x\)
\(\Rightarrow15x-10x=250+75\)
\(\Rightarrow5x=325\Rightarrow x=\frac{325}{5}=65\)
\(\left(x-8\right).\frac{3}{10}=\frac{1}{5}x+5\)
\(\frac{3}{10}x-\frac{3}{2}=\frac{1}{5}x+5\)
\(\frac{3}{10}x=\frac{1}{5}x+6,5\)
\(\Rightarrow\frac{1}{10}x=6,5\)
\(x=\frac{6,5}{\frac{1}{10}}\)
\(x=65\)
Vậy \(x=65\)
1a Để \(\frac{x+1}{2}\)=\(\frac{8}{x+1}\)
\(\Rightarrow\)x+1.(x+1)=2.8=16
\(\Rightarrow\)x+1(x+1)=4.4
suy ra x+1=4
x=4-1
x=3
a) \(\frac{7x}{8}-5\left(x-9\right)=\frac{20x+1,5}{6}\)
\(\Leftrightarrow\frac{7x}{8}-\frac{40\left(x-9\right)}{8}=\frac{20x+1,5}{6}\)
\(\Leftrightarrow\frac{7x}{8}-\frac{40x-360}{8}=\frac{20x+1,5}{6}\)
\(\Leftrightarrow\frac{360-33x}{8}=\frac{20x+1,5}{6}\)
\(\Leftrightarrow2160-198x=160x+12\)
\(\Leftrightarrow358x=2148\)
\(\Leftrightarrow x=6\)
Vậy nghiệm của pt x=6
b) \(\frac{5\left(x-1\right)+2}{6}-\frac{7x-1}{4}=\frac{2\left(2x+1\right)}{7}-5\)
\(\Leftrightarrow\frac{10\left(x-1\right)+4}{12}-\frac{21x-3}{12}=\frac{4x+2}{7}-\frac{35}{7}\)
\(\Leftrightarrow\frac{-11x-3}{12}=\frac{4x-33}{7}\)
\(\Leftrightarrow-77x-21=48x-396\)
\(\Leftrightarrow125x=375\)
\(\Leftrightarrow3\)
Vậy nghiệm của pt x=3
a: \(\Leftrightarrow\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+....+\dfrac{1}{9}-\dfrac{1}{10}\right)\cdot\left(x-1\right)+\dfrac{1}{10}x-x=-\dfrac{9}{10}\)
\(\Leftrightarrow\dfrac{9}{10}x-\dfrac{9}{10}-\dfrac{9}{10}x=-\dfrac{9}{10}\)
=>-9/10=-9/10(luôn đúng)
b: \(\Leftrightarrow\dfrac{195x+195+130x+195+117x+195+100x+195}{195}=\dfrac{22\cdot39+4\cdot65+6\cdot39+40\cdot5}{195}\)
=>347x+780=1552
=>347x=772
hay x=772/347
a/ Ta có
\(K^4+\frac{1}{4}=K^4+K^2+\frac{1}{4}-K^2=\left(K^2+\frac{1}{2}\right)^2-K^2=\left(K^2+K+\frac{1}{2}\right)\left(K^2-K+\frac{1}{2}\right)\)
Ta lại có
\(K^2+K+\frac{1}{2}=\left(K+1\right)^2-\left(K+1\right)+\frac{1}{2}\)
\(\Rightarrow K^4+\frac{1}{4}=\left(K^2-K+\frac{1}{2}\right)\left(\left(K+1\right)^2-\left(K+1\right)+\frac{1}{2}\right)\)
Áp dụng vào bài toán ta được
\(=\frac{101^2-101+0,5}{1^2-1+0,5}=20201\)\(1S=\frac{\left(2^2-2+0,5\right)\left(3^2-3+0,5\right)\left(4^2-4+0,5\right)\left(5^2-5+0,5\right)...\left(100^2-100+0,5\right)\left(101^2-101+0,5\right)}{\left(1^2-1+0,5\right)\left(2^2-2+0,5\right)\left(3^2-3+0,5\right)\left(4^2-4+0,5\right)...\left(99^2-99+0,5\right)\left(100^2-100+0,5\right)}\)
b/
\(\frac{3\left(x+y\right)}{3\sqrt{x\left(4x+5y\right)}+3\sqrt{y\left(4y+5x\right)}}\)
\(\ge\frac{3\left(x+y\right)}{\frac{9x+4x+5y}{2}+\frac{9y+4y+5x}{2}}\)
\(=\frac{1}{3}\)
Dấu = xảy ra khi x = y