( 2x - 5 ) . ( x + 9 ) + 6 x = 30
( x + 3 ) . ( 5 x - 15 ) + 2 x - 6 = 0
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a) |2x-3|+x=21
|2x-3|=21-x
\(\Rightarrow\)\(\orbr{\begin{cases}2x-3=21-x\\2x-3=-\left(21-x\right)\end{cases}}\)
TH1: 2x-3=21-x
2x-x=21+3
x=24
TH2: 2x-3=-(21-x)
2x-3 = -21+x
2x-x=-21+3
x=-18
Vậy x \(\varepsilon\){-18;24}
a) \(\left(9^4.8+9^4.5\right):\left(9^2.\left(10-1\right)\right)\)
=\(9^4.13:9^3=13.9=117\)
b) 100-(75-25)=100-50=50
a) \(x+xy-y=8\)
\(\Leftrightarrow x.\left(1+y\right)-y=8\)
\(\Leftrightarrow x.\left(1+y\right)-y-1=8-1\)
\(\Leftrightarrow x.\left(1+y\right)-\left(1+y\right)=7\)
\(\Leftrightarrow\left(1+y\right).\left(x-1\right)=7\)
Lập bảng tìm tiếp
b) Ta có: \(\hept{\begin{cases}\left(x+2\right)^2\ge0\forall x\\\left(2y-6\right)^4\ge0\forall x\end{cases}}\)
\(\Rightarrow\left(x+2\right)^2+\left(2y-6\right)^4\ge0\forall x\)
Do đó \(\left(x+2\right)^2+\left(2y-6\right)^4=0\)
\(\Leftrightarrow\hept{\begin{cases}\left(x+2\right)^2=0\\\left(2y-6\right)^4=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=-2\\y=3\end{cases}}}\)
Vậy ...
Bài 2
\(a,\left(x-5\right)^4=\left(x-5\right)^6\)
\(\Rightarrow\left(x-5\right)^6-\left(x-5\right)^4=0\)
\(\Rightarrow\left(x-5\right)^4\left[\left(x-5\right)^2-1\right]=0\)
\(\Rightarrow\left(x-5\right)^4\left(x-5+1\right)\left(x-5-1\right)=0\)
\(\Rightarrow\left(x-5\right)^4\left(x-4\right)\left(x-6\right)=0\)
\(\Rightarrow x\in\left\{4;5;6\right\}\)
\(b,\left(2x-15\right)^5=\left(2x-15\right)^3\)
\(\Rightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\)
\(\Rightarrow\left(2x-15\right)^3\left[\left(2xs-15\right)^2-1\right]=0\)
\(\Rightarrow\left(2x-15\right)^3\left(2x-15+1\right)\left(2x-15-1\right)=0\)
\(\Rightarrow\left(2x-15\right)^3\left(2x-14\right)\left(2x-16\right)\)
\(\Rightarrow x\in\left\{\frac{15}{2};7;8\right\}\)
Mà \(\frac{15}{2}\notin n\)
\(\Rightarrow x\in\left\{7;8\right\}\)
#)Giải :
Bài 1 :
a)\(A=\frac{2^{13}+2^5}{2^{10}+2^2}=\frac{2^5\left(2^8+1\right)}{2^2\left(2^8+1\right)}=2^3=8\)
b)\(B=\frac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}=\frac{11.3^{29}-3^{30}}{2^2.3^{28}}=\frac{11.3^{29}-3^{29}.3}{2^2.3^{28}}=\frac{3^{29}\left(11-3\right)}{2^2.3^{28}}=\frac{3^{29}.2^3}{2^2.3^{28}}=6\)
Bài 2 :
a) \(\left(x-5\right)^2=\left(x-5\right)^6\)
\(\Leftrightarrow x^4-625=x^6-15625\)
\(\Leftrightarrow x^6-x^4=15000\)
\(\Leftrightarrow x^6-x^4=5^6-5^4\)
\(\Leftrightarrow x=5\)
b)\(\left(2x-15\right)^5=\left(2x-15\right)^3\)
\(\Leftrightarrow2x-15=1\)
\(\Leftrightarrow2x=16\)
\(\Leftrightarrow x=8\)