( 62x-1 + 36x ) . 5 = 63 . 35
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1.
$\sqrt{3x^2}-\sqrt{12}=0$
$\Leftrightarrow \sqrt{3x^2}=\sqrt{12}$
$\Leftrightarrow 3x^2=12$
$\Leftrightarrow x^2=4$
$\Leftrightarrow (x-2)(x+2)=0\Leftrightarrow x=\pm 2$
2.
$\sqrt{(x-3)^2}=9$
$\Leftrightarrow |x-3|=9$
$\Leftrightarrow x-3=9$ hoặc $x-3=-9$
$\Leftrightarrow x=12$ hoặc $x=-6$
Ta có:
\(x=35\)
\(\Rightarrow\left\{{}\begin{matrix}x+1=36\\x+2=27\\2x-1=69\\x-1=34\end{matrix}\right.\) (1)
Thay (1) vào biểu thức ta được:
\(x^5-\left(x+1\right)x^4+\left(x+2\right)x^3-\left(2x-1\right)x^2-\left(x-1\right)x+15\)
\(=x^5-x^5-x^4+x^4+2x^3-2x^3+x^2-x^2+x+15\)
\(=x+15\)
\(=35+15\)
\(=50\)
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) \(\Leftrightarrow4\sqrt{x+1}=-4-5x\) \(\left(x\le-\dfrac{4}{5}\right)\)
\(\Leftrightarrow16\left(x+1\right)=25x^2+40x+16\)
\(\Leftrightarrow25x^2+24x=0\Rightarrow\left[{}\begin{matrix}x=0\left(loại\right)\\x=-\dfrac{24}{25}\end{matrix}\right.\)
[ 1/5 + 1/35 + 1/63 ] x [ x-2 ] =1
\(\frac{63+9+5}{315}x\left(x-2\right)=1\)
\(\frac{77}{315}x\left(x-2\right)=1\)
\(\frac{11}{45}x\left(x-2\right)=1\)
\(x-2=1:\frac{11}{45}=\frac{45}{11}\)
\(x=\frac{45}{11}+2=\frac{67}{11}\)
\(\left(\frac{1}{5}+\frac{1}{35}+\frac{1}{63}\right)\times\left(x-2\right)=1\)
\(\frac{11}{45}\times\left(x-2\right)=1\)
\(x-2=\frac{45}{11}\)
\(x=\frac{67}{11}\)