tìm x
3x - 3 - căn( x - 1) = 6
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Sửa đề bài 1 : k => x P/s : đề sai r :))
\(A=\left(3-2x\right)3x^2-8+\left(2x+5\right)\left(3x-2\right)-20x\)
\(=9x^2-6x^3-8+6x^2-4x+15x-10-20x=15x^2-6x^3-18-9x\)
Vậy biểu thức phụ thuộc biến x
\(B=\left(3-5x\right)\left(2x+11\right)-\left(2x+3\right)\left(3x+7\right)\)
\(=6x+33-10x^2-55x-6x^2-14x-9x-21=-72x+12-16x^2\)
Vậy biểu thức phụ thuộc biến x
Bài 2 :
a, \(2x\left(x-1\right)-x^2+6=0\Leftrightarrow2x^2-2x-x^2+6=0\)
\(\Leftrightarrow x^2-2x+6=0\)( vô nghiệm )
b, \(\left(x+3\right)\left(x^2-3x+9\right)-x\left(x-2\right)\left(x+2\right)=15\)
\(\Leftrightarrow\left(x+3\right)\left(x-3\right)-x\left(x-2\right)\left(x+2\right)=15\)
\(\Leftrightarrow x^2-9-x\left(x^2-4\right)=15\Leftrightarrow x^2-9-x^3+12=15\)
\(\Leftrightarrow-x^3+x^2-12=0\Leftrightarrow x=2\)
\(x^3-3\left(m+1\right)x^2+2mx+m+2=0\left(1\right)\)
\(\Leftrightarrow\left(x-1\right)\left(x^2-3mx-2x-m-2\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[x^2-x\left(3m+2\right)-m-2\right]=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x^2-x\left(3m+2\right)-m-2=0\left(2\right)\end{matrix}\right.\)
\(\left(1\right)có\) \(3ngo\) \(phân\) \(biệt\Leftrightarrow\left(2\right)\) \(có\) \(2\) \(ngo\) \(phân\) \(biệt\ne1\)
\(\Leftrightarrow\left\{{}\begin{matrix}g\left(1\right)\ne0\\\Delta>0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}m\ne\dfrac{-3}{4}\\\left(3m+2\right)^2-4\left(-m-2\right)>0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m\ne\dfrac{-3}{4}\\9m^2+16m+12>0\left(luôn-đúng\right)\end{matrix}\right.\)
\(\Rightarrow m\ne\dfrac{-3}{4}\) \(thì\left(1\right)\) \(có\) \(3ngo\) \(phân\) \(biệt\)
\(do\left(2\right)\) \(\) \(có\) \(2\) \(ngo\) \(phân\) \(biệt\ne1\Rightarrow x3=1\)
\(\Rightarrow x1+x2=2\)
\(vi-ét\Rightarrow\left\{{}\begin{matrix}x1+x2=3m+2\\x1x2=-m-2\end{matrix}\right.\)
\(\Rightarrow3m+2=2\Leftrightarrow m=0\left(tm\right)\)
\(a_1,\sqrt{x}< 7\\ \Rightarrow x< 49\\ a_2,\sqrt{2x}< 6\\ \Rightarrow x< 18\\ a_3,\sqrt{4x}\ge4\\ \Rightarrow4x\ge16\\ \Rightarrow x\ge4\\ a_4,\sqrt{x}< \sqrt{6}\\ \Rightarrow x< 6\)
\(b_1,\sqrt{x}>4\\ \Rightarrow x>16\\ b_2,\sqrt{2x}\le2\\ \Rightarrow2x\le4\\ \Rightarrow x\le2\\ b_3,\sqrt{3x}\le\sqrt{9}\\ \Rightarrow3x\le9\\ \Rightarrow x\le3\\ b_4,\sqrt{7x}\le\sqrt{35}\\ \Rightarrow7x\le35\\ \Rightarrow x\le5\)
b: ĐKXĐ: \(x\in R\)
c: ĐKXĐ: \(\left[{}\begin{matrix}x\ge1\\x\le0\end{matrix}\right.\)
a: \(A=\dfrac{2\sqrt{a}-9}{a-5\sqrt{a}+6}-\dfrac{\sqrt{a}+3}{\sqrt{a}-2}-\dfrac{2\sqrt{a}-1}{3-\sqrt{a}}\)
\(=\dfrac{2\sqrt{a}-9-\left(\sqrt{a}+3\right)\left(\sqrt{a}-3\right)+\left(2\sqrt{a}-1\right)\left(\sqrt{a}-2\right)}{\left(\sqrt{a}-2\right)\left(\sqrt{a}-3\right)}\)
\(=\dfrac{2\sqrt{a}-9-a+9+2a-5\sqrt{a}+2}{\left(\sqrt{a}-2\right)\cdot\left(\sqrt{a}-3\right)}\)
\(=\dfrac{a-3\sqrt{a}+2}{\left(\sqrt{a}-2\right)\left(\sqrt{a}-3\right)}=\dfrac{\sqrt{a}-1}{\sqrt{a}-3}\)
b: A là số nguyên
=>\(\sqrt{a}-3+2⋮\sqrt{a}-3\)
=>\(\sqrt{a}-3\in\left\{1;-1;2;-2\right\}\)
=>a thuộc {16;25;1}
ai gúp pé yk