Tìm các số hữu tỉ x , sao cho :
a) \(\left|\text{x}-5\right|-\text{x}=3\)
b) \(\text{ }\left|\text{x}\right|+\frac{-1}{4}=\frac{-3}{12}\)
c) \(-\left|\text{x}\right|+\frac{2}{3}=0\)
d) \(\left|x-3\right|=3\)
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Bài 1:
\(A=\sqrt{5-2\sqrt{6}}+\sqrt{5+2\sqrt{6}}=\sqrt{2+3-2\sqrt{2.3}}+\sqrt{2+3+2\sqrt{2.3}}\)
\(=\sqrt{(\sqrt{2}-\sqrt{3})^2}+\sqrt{\sqrt{2}+\sqrt{3})^2}\)
\(=|\sqrt{2}-\sqrt{3}|+|\sqrt{2}+\sqrt{3}|=\sqrt{3}-\sqrt{2}+\sqrt{2}+\sqrt{3}=2\sqrt{3}\)
\(B=(\sqrt{10}+\sqrt{6})\sqrt{8-2\sqrt{15}}\)
\(=(\sqrt{10}+\sqrt{6}).\sqrt{3+5-2\sqrt{3.5}}\)
\(=(\sqrt{10}+\sqrt{6})\sqrt{(\sqrt{5}-\sqrt{3})^2}\)
\(=\sqrt{2}(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})=\sqrt{2}(5-3)=2\sqrt{2}\)
\(C=\sqrt{4+\sqrt{7}}+\sqrt{4-\sqrt{7}}\)
\(C^2=8+2\sqrt{(4+\sqrt{7})(4-\sqrt{7})}=8+2\sqrt{4^2-7}=8+2.3=14\)
\(\Rightarrow C=\sqrt{14}\)
\(D=(3+\sqrt{5})(\sqrt{5}-1).\sqrt{2}\sqrt{3-\sqrt{5}}\)
\(=(3+\sqrt{5})(\sqrt{5}-1).\sqrt{6-2\sqrt{5}}\)
\(=(3+\sqrt{5})(\sqrt{5}-1).\sqrt{5+1-2\sqrt{5.1}}\)
\(=(3+\sqrt{5})(\sqrt{5}-1).\sqrt{(\sqrt{5}-1)^2}\)
\(=(3+\sqrt{5})(\sqrt{5}-1)^2=(3+\sqrt{5})(6-2\sqrt{5})=2(3+\sqrt{5})(3-\sqrt{5})=2(3^2-5)=8\)
Bài 2:
a) Bạn xem lại đề.
b) \(x-2\sqrt{xy}+y=(\sqrt{x})^2-2\sqrt{x}.\sqrt{y}+(\sqrt{y})^2=(\sqrt{x}-\sqrt{y})^2\)
c)
\(\sqrt{xy}+2\sqrt{x}-3\sqrt{y}-6=(\sqrt{x}.\sqrt{y}+2\sqrt{x})-(3\sqrt{y}+6)\)
\(=\sqrt{x}(\sqrt{y}+2)-3(\sqrt{y}+2)=(\sqrt{x}-3)(\sqrt{y}+2)\)
\(\frac{5.2^{18}.3^{18}.2^{12}-2.2^{28}.3^{14}.3^4}{5.2^{28}.3^{18}-7.2^{29}.3^{18}}=\frac{5.2^{30}.3^{18}-2^{29}.3^{18}}{5.2^{28}.3^{18}-7.2^{29}.3^{18}}=\frac{2^{29}.3^{18}\left(5.2-1\right)}{2^{28}.3^{18}\left(5-7.2\right)}\)
\(\frac{2^{29}.3^{18}.9}{2^{28}.3^{18}.-9}=\frac{2.9}{-9}=-2\)
a) \(\left|x-5\right|-x=3\Leftrightarrow\left|x-5\right|=3+x\)
+)TH1: x>=5 thì pt trở thành
x-5=3+x <=> 0x=8 (vô nghiệm)
+)Th2: x<5 thì pt trở thành:
5-x=3+x <=> 2x=2 <=> x=1 (tm)
Vậy x=1
b)\(\left|x\right|+\frac{-1}{4}=\frac{-3}{12}\)
\(\Leftrightarrow\left|x\right|=0\Leftrightarrow x=0\)
c)\(-\left|x\right|+\frac{2}{3}=0\)
\(\Leftrightarrow\left|x\right|=\frac{2}{3}\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=\frac{2}{3}\\x=-\frac{2}{3}\end{array}\right.\)
d) \(\left|x-3\right|=3\)
+)TH1: x>=3 thì pt trở thành
x-3=3 <=>x=6(tm)
+)TH2: x<3 thì pt trở thành
x-3=-3 <=> x=0(tm)
Vậy x={0;6}
j vậy???? đây là sinh học mà