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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: Xét ΔAMC và ΔBMD có
MA=MB
\(\widehat{AMC}=\widehat{BMD}\)
MC=MD
Do đó: ΔAMC=ΔBMD
Bài 3:
Áp dụng tc dtsnb:
\(\dfrac{x}{5}=\dfrac{y}{3}=\dfrac{z}{4}=\dfrac{x+2y-z}{5+3\cdot2-4}=\dfrac{63}{7}=9\\ \Rightarrow\left\{{}\begin{matrix}x=45\\y=27\\z=36\end{matrix}\right.\)
Có: \(A\left(x\right)=x^4+2x^2-x\) và \(B\left(x\right)=-x^4-\dfrac{1}{2}x^2+2x-8\)
+, \(C\left(x\right)=A\left(x\right)+B\left(x\right)\)
\(=\left(x^4+2x^2-x\right)+\left(-x^4-\dfrac{1}{2}x^2+2x-8\right)\)
\(=x^4+2x^2-x-x^4-\dfrac{1}{2}x^2+2x-8\)
\(=\dfrac{3}{2}x^2+x-8\)
+, \(D\left(x\right)=B\left(x\right)-A\left(x\right)\)
\(=\left(-x^4-\dfrac{1}{2}x^2+2x-8\right)-\left(x^4+2x^2-x\right)\)
\(=-x^4-\dfrac{1}{2}x^2+2x-8-x^4-2x^2+x\)
\(=-2x^4-\dfrac{5}{2}x^2+3x-8\)
b) Ta có: \(C\left(x\right)=\dfrac{3}{2}x^2+x-8\)
\(\Rightarrow C\left(2\right)=\dfrac{3}{2}\cdot2^2+2-8=0\)
\(\Rightarrow x=2\) là 1 nghiệm của \(C\left(x\right)\)
c) Có: \(E\left(x\right)+D\left(x\right)=2x^4\)
\(\Rightarrow E\left(x\right)=2x^4-D\left(x\right)\)
\(=2x^4-\left(-2x^4-\dfrac{5}{2}x^2+3x-8\right)\)
\(=2x^4+2x^4+\dfrac{5}{2}x^2-3x+8\)
\(=4x^4+\dfrac{5}{2}x^2-3x+8\)