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\(\left(\frac{1}{13}x-7\right)^8+\left(\frac{1}{17}y-7\right)^6=0\)
\(\Leftrightarrow\hept{\begin{cases}\frac{1}{13}x-7=0\\\frac{1}{17}y-6=0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=91\\y=102\end{cases}}\)
\(x+y=91+102=193\)
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Bài 6:
Để B là số nguyên thì \(\sqrt{x}-2+3⋮\sqrt{x}-2\)
\(\Leftrightarrow\sqrt{x}-2\in\left\{1;-1;3\right\}\)
hay \(x\in\left\{9;1;25\right\}\)
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Vì \(\left(\frac{1}{13}x-7\right)^8\ge0;\left(\frac{1}{17}y-7\right)^6\ge0\)=>\(\left(\frac{1}{13}x-7\right)^8+\left(\frac{1}{17}y-7\right)^6\ge0\)
Dấu "=" xảy ra khi \(\left(\frac{1}{13}x-7\right)^8=\left(\frac{1}{17}y-7\right)^6=0\Leftrightarrow\frac{1}{13}x-7=\frac{1}{17}y-7=0\)
<=>\(\frac{1}{13}x=\frac{1}{17}y=7\Leftrightarrow x=\frac{7}{\frac{1}{13}}=91;y=\frac{7}{\frac{1}{17}}=119\Rightarrow x+y=91+119=210\)
Vậy .................
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a) Với x = 11 <=> 12 = x+1
\(A\left(x\right)=x^{17}-\left(x+1\right)x^{16}+\left(x+1\right)x^{15}-...+12x-1\)
\(A\left(x\right)=12x-11=12.11-1=120\)
b) \(B=6x-6y+10-3ax+3ay+15a\)
\(B=6\left(x-y\right)+10-3a\left(x-y\right)+15a\)
\(B=6.5+10-3.a.5+15a\)
\(B=40\)
c)\(C=\frac{x-y}{x+6}=\frac{x-y}{x+x-2y}=\frac{x-y}{2\left(x-y\right)}=\frac{1}{2}\left(x-2y=6\right)\)
\(C=\frac{2x+6}{3x-2y}+\frac{2y-6}{4y-x}\)
\(C=\frac{2x+1-2y}{3x-2y}+\frac{2y-x+2y}{4y-x}\)
\(C=1+1=2\)
d) ta có : x-y-x = 0
\(\Rightarrow\left\{{}\begin{matrix}x-z=y\\x-y=z\\x=y+z\end{matrix}\right.\).Thay vào B, ta có :
\(B=\frac{x-z}{x}.\frac{y-x}{y}.\frac{z+y}{z}\)
\(B=\frac{y}{x}.\frac{\left(-z\right)}{y}.\frac{x}{z}\)
B= -1