tính C=a^2022+3^2022/b^2022+5^2022 biết a,b khác 0 thõa mãn 3a-b=1/2(a+b)
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c, \(x\)(\(x\) - 2022) + 4.(2022 - \(x\)) = 0
(\(x\) - 2022).(\(x\) - 4) = 0
\(\left[{}\begin{matrix}x-2022=0\\x+4=0\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=2022\\x=4\end{matrix}\right.\)
3a-b=1/2(a+b)
=>6a-2b=a+b
=>5a=3b
=>a/3=b/5=k
=>a=3k; b=5k
\(A=\dfrac{a^{2022}+3^{2022}}{b^{2022}+5^{2022}}\)
\(=\dfrac{3^{2022}\left(k^{2022}+1\right)}{5^{2022}\left(k^{2022}+1\right)}=\left(\dfrac{3}{5}\right)^{2022}\)
a^2+b^2+c^2=ab+bc+ac
=>2a^2+2b^2+2c^2-2ab-2bc-2ac=0
=>a^2-2ab+b^2+b^2-2bc+c^2+a^2-2ac+c^2=0
=>(a-b)^2+(b-c)^2+(a-c)^2=0
=>a=b=c
\(T=\dfrac{a^{2022}+a^{2022}+a^{2022}}{\left(3a\right)^{2022}}=\dfrac{3}{3^{2022}}=\dfrac{1}{3^{2021}}\)
Cho a,b,c thõa mãn : a^2 + b^2 +c^2 - ab -bc- ca = 0. Tính: P = (a-b)^2020 + (b-c)^2021 + (c-a)^2022
\(a^2+b^2+c^2-ab-bc-ac=0\)
\(\Rightarrow2a^2+2b^2+2c^2-2ab-2bc-2ac=0\)
\(\Rightarrow\left(a-b\right)^2+\left(b-c\right)^2+\left(a-c\right)^2=0\) (1)
Mà: \(\left(a-b\right)^2+\left(b-c\right)^2+\left(a-c\right)^2\ge0\)
Nên PT (1) \(\Leftrightarrow\left\{{}\begin{matrix}\left(a-b\right)^2=0\\\left(b-c\right)^2=0\\\left(a-c\right)^2=0\end{matrix}\right.\)
=> a = b = c
\(P=\left(a-b\right)^{2020}+\left(b-c\right)^{2021}+\left(c-a\right)^{2022}\)
\(=\left(a-a\right)^{2020}+\left(b-b\right)^{2021}+\left(c-c\right)^{2022}\)
= 0