3 = y = -36
x 35 84
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\(\Leftrightarrow14\sqrt{x+35}+6\sqrt{x+1}-84-\sqrt{\left(x+35\right)\left(x+1\right)}=0\)
\(\Leftrightarrow\left(\sqrt{x+35}-6\right)\left(14-\sqrt{x+1}\right)=0\)
\(\Leftrightarrow x=195;1\)
tick nha
b.
ĐKXĐ: \(x\ge-1\)
\(\sqrt{\left(x+1\right)\left(x+35\right)}-14\sqrt{x+35}+84-6\sqrt{x+1}=0\)
\(\Leftrightarrow\sqrt{x+1}\left(\sqrt{x+35}-14\right)-6\left(\sqrt{x+35}-14\right)=0\)
\(\Leftrightarrow\left(\sqrt{x+1}-6\right)\left(\sqrt{x+35}-14\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x+1}=6\\\sqrt{x+35}=14\end{matrix}\right.\)
\(\Leftrightarrow...\)
a. ĐKXĐ: \(-1\le x\le1\)
Đặt \(\left\{{}\begin{matrix}\sqrt{x+1}=a\ge0\\\sqrt{1-x}=b\ge0\end{matrix}\right.\)
\(\Rightarrow a+2a^2=-b^2+b+3ab\)
\(\Leftrightarrow\left(2a^2-3ab+b^2\right)+a-b=0\)
\(\Leftrightarrow\left(a-b\right)\left(2a-b\right)+a-b=0\)
\(\Leftrightarrow\left(a-b\right)\left(2a-b+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a=b\\2a+1=b\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x+1}=\sqrt{1-x}\\2\sqrt{x+1}+1=\sqrt{1-x}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\4x+5+4\sqrt{x+1}=1-x\left(1\right)\end{matrix}\right.\)
(1) \(\Leftrightarrow4\sqrt{x+1}=-4-5x\) \(\left(x\le-\dfrac{4}{5}\right)\)
\(\Leftrightarrow16\left(x+1\right)=25x^2+40x+16\)
\(\Leftrightarrow25x^2+24x=0\Rightarrow\left[{}\begin{matrix}x=0\left(loại\right)\\x=-\dfrac{24}{25}\end{matrix}\right.\)
Ta có:
\(\dfrac{3}{x}=\dfrac{y}{35}=\dfrac{-36}{84}\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{3}{x}=\dfrac{-36}{84}\\\dfrac{y}{35}=\dfrac{-36}{84}\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}3.84=-36.x\\y.84=-36.35\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{3.84}{-36}\\y=\dfrac{-36.35}{84}\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}x=-7\\y=-15\end{matrix}\right.\)
Vậy: \(\left\{{}\begin{matrix}x=-7\\y=-15\end{matrix}\right.\)
Ta có: -36/84=-3/7
=> 3/x=y/35=-3/7
3/x=-3/7
=> 3.7=-3.x
=> 21=-3.x
=> 21:(-3)=x
=> x=-7
y/35=-3/7
=> y.7=35.(-3)
=> y.7=-105
=> y =-105:7
=> y =-15
Vậy x=-7;y=-15
Cách nhanh hơn là:-36/84=-3/7
3/x=-3/7 suy ra x=-7
y/35=-3/7suy ra y=-15
-36/84 = -3/7
3/x = -3/7 => x = -7
y/35 = -3/7 => y = -15
x=7
y=15
Tick nha !!!!!
x = 7
y = 15
kb nha