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\(x^3+2x^2\left(4y-1\right)-4xy^2-9y^3-f\left(x\right)=-5x^3+8x^2y-4xy^2-9y^3\\ \Rightarrow\left(x^3+8x^2y+2x^2-4xy^2-9y^3\right)-f\left(x\right)=-5x^3+8x^2y-4xy^2-9y^3\\ \Rightarrow f\left(x\right)=x^3+8x^2y+2x^2-4xy^2-9y^3+5x^3-8x^2y+4xy^2+9y^3\\ \Rightarrow f\left(x\right)=6x^3+2x^2\)
\(\dfrac{\sqrt{5^2}-\sqrt{19^2}}{\sqrt{8^2}-\sqrt{22^2}}=\dfrac{5-19}{8-22}=\dfrac{-14}{-14}=1\)
Bài 8:
a: Ta có: \(\left(5x+1\right)^2=\dfrac{36}{49}\)
\(\Leftrightarrow\left[{}\begin{matrix}5x+1=\dfrac{6}{7}\\5x+1=-\dfrac{6}{7}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}5x=\dfrac{-1}{7}\\5x=\dfrac{-13}{7}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-1}{35}\\x=\dfrac{-13}{35}\end{matrix}\right.\)
b: Ta có: \(\left(x-\dfrac{2}{9}\right)^3=\left(\dfrac{2}{3}\right)^6\)
\(\Leftrightarrow x-\dfrac{2}{9}=\dfrac{4}{9}\)
hay \(x=\dfrac{2}{3}\)
\(7,\\ a,=\dfrac{3^{10}\cdot3^5\cdot5^5}{5^6\cdot\left[-\left(3^7\right)\right]}=\dfrac{3^8}{-5}=-\dfrac{6561}{5}\\ b,=8+3-\dfrac{1}{4}\cdot4+\left(4:\dfrac{1}{2}\right)\cdot8\\ =8+3-1+64=74\\ 8,\\ a,\left(5x+1\right)^2=\dfrac{36}{49}\Rightarrow\left[{}\begin{matrix}5x+1=\dfrac{6}{7}\\5x+1=-\dfrac{6}{7}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-\dfrac{1}{35}\\x=-\dfrac{13}{35}\end{matrix}\right.\)
\(b,\Rightarrow8x-1=5\Rightarrow x=\dfrac{3}{4}\\ d,\Rightarrow\left\{{}\begin{matrix}x-3,5=0\\y-\dfrac{1}{10}=0\end{matrix}\right.\left[\left(x-3,5\right)^2\ge0;\left(y-\dfrac{1}{10}\right)^4\ge0\right]\\ \Rightarrow\left\{{}\begin{matrix}x=3,5\\y=\dfrac{1}{10}\end{matrix}\right.\)
a: góc DAC=90-40=50 độ
b: góc ADB=90 độ
c: góc DAB=90-80=10 độ
=>góc BAE=10+50=60 độ
góc AED=180-60=120 độ
\(a,1-\left(\dfrac{\dfrac{5}{3}}{8}+x-\dfrac{\dfrac{7}{5}}{24}\right)-\dfrac{\dfrac{16}{2}}{3}=0\\ \Leftrightarrow1-\left(\dfrac{5}{24}+x-\dfrac{7}{120}\right)=\dfrac{8}{3}\\ \Leftrightarrow\dfrac{3}{20}+x=1-\dfrac{8}{3}=-\dfrac{5}{3}\\ \Leftrightarrow x=-\dfrac{5}{3}-\dfrac{3}{20}=-\dfrac{109}{60}\)
Ta có: Om là phân giác của góc xOy
=>\(\widehat{yOm}=\dfrac{\widehat{xOy}}{2}\)
On là phân giác của góc yOz
=>\(\widehat{yOn}=\dfrac{\widehat{yOz}}{2}\)
\(\widehat{mOn}=\widehat{yOm}+\widehat{yOn}=\dfrac{\widehat{xOy}}{2}+\dfrac{\widehat{yOz}}{2}=\dfrac{180^0}{2}=90^0\)
=>Om\(\perp\)On