Giúp mình câu 6 với . Cảm ơn nhiều!
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\(\Leftrightarrow16x^4-4x^2-4xy+y^2+1=0\)
\(\Leftrightarrow\left(16x^4-8x^2+1\right)+\left(4x^2-4xy+y^2\right)=0\)
\(\Leftrightarrow\left(4x^2-1\right)^2+\left(2x-y\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}4x^2-1=0\\2x-y=0\end{matrix}\right.\)
\(\Leftrightarrow\left(x;y\right)=\left(-\dfrac{1}{2};-1\right);\left(\dfrac{1}{2};1\right)\)
1. While I was staying in Paris last summer, I met her.
2. When we were having dinner, there was a knock at the door.
3. When did you start studying English.
4. He used to visit me on Sundays when he studied in England.
5. Saving some pocket money for charity work is meaningful.
6. Our children find it interesting to give away their old books to needy people.
7. It's a year since we last saw Mary.
\(a,m=3\Leftrightarrow y=2x+2\\ A\left(a;-4\right)\in\left(d\right)\Leftrightarrow2a+2=-4\Leftrightarrow a=-3\)
\(b,\) PT giao Ox của (d) là \(2x+m-1=0\Leftrightarrow x=\dfrac{1-m}{2}\Leftrightarrow M\left(\dfrac{1-m}{2};0\right)\Leftrightarrow OM=\dfrac{\left|1-m\right|}{2}\)
PT giao Oy của (d) là \(x=0\Leftrightarrow y=m-1\Leftrightarrow N\left(0;m-1\right)\Leftrightarrow ON=\left|m-1\right|\)
Để \(S_{OMN}=1\Leftrightarrow\dfrac{1}{2}OM\cdot ON=1\Leftrightarrow OM\cdot ON=2\)
\(\Leftrightarrow\dfrac{\left|\left(1-m\right)\left(m-1\right)\right|}{2}=2\\ \Leftrightarrow\left|-\left(m-1\right)^2\right|=2\\ \Leftrightarrow\left(m-1\right)^2=2\\ \Leftrightarrow\left[{}\begin{matrix}m=1+\sqrt{2}\\m=1-\sqrt{2}\end{matrix}\right.\)
3d:
20<x<45
x chia 4 dư 1 nên x-1 thuộc B(4)
=>\(x-1\in\left\{0;4;...;44;48\right\}\)
=>\(x\in\left\{1;5;...;45;49\right\}\)
mà 20<x<45
nên x thuộc {21;26;31;35;41}
4:
a: A={x∈N|51<=x<=127}
b: B={x∈N|100<=x<=999}
c: C={x∈N|x=7k+5; 0<=k<=8}