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\(\left(74.25+\dfrac{3}{4}\right)\times x-131.5=18.5\)
\(\left(74.25+0.75\right)\times x=18.5+131.5\)
\(75\times x=150\)
\(x=150:75\)
\(x=2\)
`(74,25 + 3/4) xx x-131,5 =18,5`
`75xx x=18,5 + 131,5`
`75 xx x =150`
`x=150:75`
`x = 2`
a: 461+(x-45)=387
=>\(x-45=387-461=-74\)
=>\(x=-74+45=-29\)
b: \(15\cdot23-85\cdot23+\left|x-1\right|=2200\)
=>\(23\cdot\left(15-85\right)+\left|x-1\right|=2200\)
=>\(23\cdot\left(-70\right)+\left|x-1\right|=2200\)
=>\(\left|x-1\right|=2200+23\cdot70=3810\)
=>\(\left[{}\begin{matrix}x-1=3810\\x-1=-3810\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3811\\x=-3809\end{matrix}\right.\)
c: \(11-\left(-53+x\right)=97\)
=>\(11+53-x=97\)
=>64-x=97
=>x=64-97=-33
d: \(-\left|x-\left(-4\right)\right|=-9\)
=>\(\left|x-\left(-4\right)\right|=9\)
=>\(\left|x+4\right|=9\)
=>\(\left[{}\begin{matrix}x+4=9\\x+4=-9\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-13\end{matrix}\right.\)
e: \(-\left(x+84\right)+213=-16\)
=>\(213-x-84=-16\)
=>\(129-x=-16\)
=>x=129+16=145
f: \(-\left(15-x\right)=2^5:2^3\)
=>\(x-15=2^2=4\)
=>x=4+15=19
`a, 461+(x-45)=387`
`<=> x-45=461-387`
`<=> x-45=74`
`<=> x=74+45=119`.
Vậy `x=119.`
`b, 15.23-85.23+|x-1|=2200`
`<=> 23.(15-85)+|x-1|=2200`
`<=> 23.(-60)+|x-1|=2200`
`<=> |x-1|=3580`
`<=> x=3581` hoặc `x=-3579.`
a) \(2a=3b=4c\)
\(\Rightarrow\dfrac{a}{6}=\dfrac{b}{4}=\dfrac{c}{3}\)
Áp dụng t/c dtsbn:
\(\dfrac{a}{6}=\dfrac{b}{4}=\dfrac{c}{3}=\dfrac{a-b+c}{6-4+3}=\dfrac{35}{5}=7\)
\(\Rightarrow\left\{{}\begin{matrix}a=7.6=42\\b=7.4=28\\c=7.3=21\end{matrix}\right.\)
b) \(21x=19y\Rightarrow\dfrac{x}{19}=\dfrac{y}{21}\)
Áp dụng t/c dtsbn:
\(\dfrac{x}{19}=\dfrac{y}{21}=\dfrac{2x}{38}=\dfrac{y-2x}{21-38}=\dfrac{-34}{-17}=2\)
\(\Rightarrow\left\{{}\begin{matrix}x=2.19=38\\y=2.21=42\end{matrix}\right.\)
\(2x-49=5.32\\ \Leftrightarrow2x-49=160\\ \Leftrightarrow2x=209\\ \Leftrightarrow x=\dfrac{209}{2}\)
\(200-\left(2x+6\right)=43\\ \Leftrightarrow2x+6=157\\ \Leftrightarrow2x=151\\ \Leftrightarrow x=\dfrac{151}{2}\)
\(135-5\left(x+4\right)=35\\ \Leftrightarrow5\left(x+4\right)=100\\ \Leftrightarrow x+4=20\\ \Leftrightarrow x=16\)
\(\Leftrightarrow164-4\left(x-5\right)=80\\ \Leftrightarrow4\left(x-5\right)=84\\ \Leftrightarrow x-5=21\Leftrightarrow x=26\)
x x 3 + : 0,5=12,8
x x (3 + 2)=12,8
x x 5=12,8
x = 12,8 :5
x = 2,56
1.
Đặt \(x-2=t\ne0\Rightarrow x=t+2\)
\(B=\dfrac{4\left(t+2\right)^2-6\left(t+2\right)+1}{t^2}=\dfrac{4t^2+10t+5}{t^2}=\dfrac{5}{t^2}+\dfrac{2}{t}+4=5\left(\dfrac{1}{t}+\dfrac{1}{5}\right)^2+\dfrac{19}{5}\ge\dfrac{19}{5}\)
\(B_{min}=\dfrac{19}{5}\) khi \(t=-5\) hay \(x=-3\)
2.
Đặt \(x-1=t\ne0\Rightarrow x=t+1\)
\(C=\dfrac{\left(t+1\right)^2+4\left(t+1\right)-14}{t^2}=\dfrac{t^2+6t-9}{t^2}=-\dfrac{9}{t^2}+\dfrac{6}{t}+1=-\left(\dfrac{3}{t}-1\right)^2+2\le2\)
\(C_{max}=2\) khi \(t=3\) hay \(x=4\)
a) x6 + x4 = 0
=> x4 . ( x2 + 1 ) = 0
\(\Rightarrow\hept{\begin{cases}x^4=0\\x^2+1=0\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x=0\\x^2=-1\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x=0\\x∈Ø \left(\text{ do }x^2≥0∀x\right)\end{cases}}\)
b) \(\left|-x+\frac{5}{3}\right|-2=3\frac{1}{3}\)
\(\Rightarrow\left|\frac{5}{3}-x\right|=3\frac{1}{3}+2=5\frac{1}{3}\)
\(\Rightarrow\orbr{\begin{cases}\frac{5}{3}-x=5\frac{1}{3}\\\frac{5}{3}-x=-5\frac{1}{3}\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{5}{3}-5\frac{1}{3}\\x=\frac{5}{3}-\left(-5\frac{1}{3}\right)\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=-\frac{11}{3}\\x=7\end{cases}}\)