Tìm x biết (5/6)^2*x+17=3125/7776
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a) \(2^x.4=128\Rightarrow2^x=32=2^5\Rightarrow x=5\)
b) \(x^{17}=x\Rightarrow x^{17}-x=0\Rightarrow x\left(x^{16}-1\right)=0\Rightarrow x=0\) hay \(x=1\)
c) \(\left(2x-2\right)^3=8\Rightarrow\left(2x-2\right)^3=2^3\Rightarrow2x-2=2\Rightarrow2x=4\Rightarrow x=2\)
d) \(\left(x-6\right)^3=\left(x-6\right)^2\Rightarrow\left(x-6\right)^3-\left(x-6\right)^2=0\)
\(\Rightarrow\left(x-6\right)^2\left(x-6-1\right)=0\Rightarrow\Rightarrow\left(x-6\right)^2\left(x-7\right)=0\)
\(\Rightarrow x-6=0\) hay \(x-7=0\Rightarrow x=6\) hay \(x=7\)
e) \(\left(7x-11\right)^3=2^5.5^2+200\Rightarrow\left(7x-11\right)^3=32.25+200\)
\(\Rightarrow\left(7x-11\right)^3=1000=10^3\Rightarrow7x-11=10\Rightarrow7x=21\Rightarrow x=3\)
f) \(3+2^{x-1}=24-\left[4^2-\left(2^2-1\right)\right]\Rightarrow2^{x-1}=24-\left[16-3\right]-3\)
\(\Rightarrow2^{x-1}=24-13-3\Rightarrow2^{x-1}=8=2^3\Rightarrow2x-1=3\Rightarrow2x=4\Rightarrow x=2\)
Bài giải
a, \(-\left(-x\right)-\left(-9\right)=-\left(3-6-9+3\right)\)
\(x+9=-3+6+9-3\)
\(x+9=15\)
\(x=15-9\)
\(x=6\)
b, \(17-x=7-6x\)
\(6x-x=7-17\)
\(5x=-10\)
\(x=-10\text{ : }5\)
\(x=-2\)
c, \(5x-7=-21-2x\)
\(5x+2x=-21+7\)
\(7x=-14\)
\(x=-14\text{ : }7\)
\(x=-2\)
d, \(7\left(x-3\right)-5\left(3-x\right)=11x-5\)
\(7x-21-15+5x=11x-5\)
\(7x+5x-11x=21+15-5\)
\(x=31\)