Tính nhiệm:
x2+6x+15
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4(x - 1) + 6x \(\le\) 3(x + 1) + 15
<=> 4x - 4 + 6x \(\le\) 3x + 3 + 15
<=> 7x \(\le\) 22
<=> x \(\le\) \(\dfrac{22}{7}\) S = {x|x\(\le\) \(\dfrac{22}{7}\)}
4(x-1) + 6x ≤ 3(x+1) + 15
<=> 4x + 6x - 3x ≤ 3 + 15 + 4
<=> 7x ≤ 22 <=> x ≤ 22/7
a/ Ta có \(\sqrt{x^2-6x+22}+\sqrt{x^2-6x+10}=4\)
\(\Leftrightarrow\left(\sqrt{x^2-6x+22}+\sqrt{x^2-6x+10}\right)\left(\sqrt{x^2-6x+22}-\sqrt{x^2-6x+10}\right)=4A\)
\(\Leftrightarrow4A=\left(x^2-6x+22\right)-\left(x^2-6x+10\right)\)
\(\Leftrightarrow4A=12\Leftrightarrow A=3\)
b/ Tương tự.
\(1,\\ a,=-35x^5y^4z\\ b,=6x^2-30x-6x^2-3x=-33x\\ c,=x^3-9x^2-2x^2+18x-x+9=x^3-11x^2+17x+9\\ 2,\\ A\left(x\right)+B\left(x\right)=10-2x+4x^3-5x^2-10x^3-5x+6x^2-20\\ =-6x^3+x^2-7x-10\\ A\left(x\right)-B\left(x\right)=10-2x+4x^3-5x^2+10x^3+5x-6x^2+20\\ =14x^3-11x^2+3x+30\\ 3,\\ a,M\left(x\right)=5x+20=0\\ \Leftrightarrow x=-4\\ b,N\left(x\right)=100x^2-49=0\\ \Leftrightarrow\left(10x-7\right)\left(10x+7\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{10}\\x=-\dfrac{7}{10}\end{matrix}\right.\\ c,P\left(x\right)=3x-15=0\\ \Leftrightarrow x=5\)
Bài 1;
a)\(5x^3yz.\left(-7x^2y^3\right)=-35.x^5y^4z\)
b)\(6x\left(x-5\right)-x\left(6x+3\right)=6x^2-30x-6x^2-3x=-33x\)
c) \(\left(x-9\right)\left(x^2-2x-1\right)=x^3-2x^2-x-9x^2+18x+9=x^3-11x^2+17x+9\)
\(\dfrac{x^2-6x+15}{x^2-6x+11}=\sqrt{x^2-6x+18}\)
\(\Leftrightarrow1+\dfrac{4}{x^2-6x+11}=\sqrt{\left(x-3\right)^2+9}\)
Ta có: \(x^2-6x+11=\left(x-3\right)^2+2\ge2\)
\(\Rightarrow VT=1+\dfrac{4}{x^2-6x+11}\le1+\dfrac{4}{2}=3\)
\(VP=\sqrt{\left(x-3\right)^2+9}\ge3\)
D=xrk x=3
Kl: x=3
Đặt \(x^2-6x+18=t\)\(\left(t\ge9\right)\)
\(\Rightarrow\dfrac{t-3}{t-7}=\sqrt{t}\)
\(\Leftrightarrow t\sqrt{t}-7\sqrt{t}=t-3\)
\(\Leftrightarrow\left(\sqrt{t}\right)^3-t-7\sqrt{t}+3=0\)
\(\Leftrightarrow\left(\sqrt{t}-3\right)\left(t+2\sqrt{t}-1\right)=0\)
Ta Thấy :
\(t+2\sqrt{t}-1\) có 2 nghiệm là \(\left\{-\left(\sqrt{2}+1\right);\left(\sqrt{2}-1\right)\right\}\)đều nhỏ hơn 9
Nên \(\sqrt{t}=3\Leftrightarrow t=9\left(tm\right)\)
\(\Rightarrow x^2-6x+18=9\)
\(\Leftrightarrow x^2-6x+9=0\)
\(\Leftrightarrow\left(x-3\right)^2=0\Leftrightarrow x=3\)
Vậy Phương trình đã cho có nghiệm x = 3 .