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AH=căn 6^2-4,8^2=3,6cm
=>AC=6^2/3,6=10cm
Câu 2:
Ta có: \(\sqrt{x^2-4x+4}=x-1\)
\(\Leftrightarrow2-x=x-1\left(x< 2\right)\)
\(\Leftrightarrow-2x=-3\)
hay \(x=\dfrac{3}{2}\left(tm\right)\)
\(26,\\ a,\sin45^0=\cos45^0< \sin50^025'< \sin57^048'=\cos32^012'< \sin72^0=\cos18^0< \sin75^0\\ b,\tan37^026'< \tan47^0< \tan58^0=\cot32^0< \tan63^0< \tan66^019'=\cot23^041'\\ 27,\\ A=\dfrac{\left(\sin^226^0+\sin^264^0\right)+2\left(\cos^215^0+\cos^275^0\right)}{\left(\sin^255^0+\cos^255^0\right)+\left(\sin^242^0+\cos^242^0\right)}-\dfrac{\tan81^0}{2\tan81^0}\\ A=\dfrac{\left(\sin^226^0+\cos^226^0\right)+2\left(\sin^215^0+\cos^215^0\right)}{1+1}-\dfrac{1}{2}\\ A=\dfrac{1+2}{2}-\dfrac{1}{2}=2-\dfrac{1}{2}=\dfrac{3}{2}\)
\(28,\\ \sin^2\alpha=1-\cos^2\alpha=1-\dfrac{1}{2}=\dfrac{1}{2}\\ \Leftrightarrow\sin\alpha=\dfrac{\sqrt{2}}{2}\)
\(n=\sqrt{2}\left(\sqrt{3}+1\right)\sqrt{2-\sqrt{3}}\\ n=\left(\sqrt{3}+1\right)\sqrt{4-2\sqrt{3}}\\ n=\left(\sqrt{3}+1\right)\sqrt{\left(\sqrt{3}-1\right)^2}\\ n=\left(\sqrt{3}+1\right)\left|\sqrt{3}-1\right|\\ n=\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)\\ n=3-1=2\)
Theo Vi-et, ta có:
\(\left\{{}\begin{matrix}x_1+x_2=-\dfrac{b}{a}=4\\x_1x_2=\dfrac{c}{a}=2\end{matrix}\right.\)
\(x_1>x_2\)
=>\(x_1-x_2>0\)
\(\left(x_1-x_2\right)^2=\left(x_1+x_2\right)^2-4x_1x_2\)
\(=4^2-4\cdot2=8\)
=>\(x_1-x_2=2\sqrt{2}\)(do x1-x2>0)
\(P=\dfrac{1}{x_1^2}-\dfrac{1}{x_2^2}+2024\)
\(=\dfrac{x_2^2-x_1^2}{\left(x_1x_2\right)^4}+2024\)
\(=\dfrac{\left(x_2-x_1\right)\left(x_2+x_1\right)}{2^4}+2024\)
\(=\dfrac{\left(x_2-x_1\right)\cdot4}{16}+2024=\dfrac{\left(x_2-x_1\right)}{4}+2024\)
\(=\dfrac{-2\sqrt{2}}{4}+2024=-\dfrac{\sqrt{2}}{2}+2024=\dfrac{4048-\sqrt{2}}{2}\)