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a: x^2+10x+100
=x^2+10x+25+75=(x+5)^2+75>0 với mọi x
b: -x^2+4x-100
=-(x^2-4x+100)
=-(x^2-4x+4+96)
=-(x-2)^2-96<0 với mọi x
c: x^2-5x+6
=x^2-5x+25/4-1/4
=(x-5/2)^2-1/4 chưa chắc lớn hơn 0 đâu nha bạn
2D
6
\(x^3+125=\left(x+5\right)\left(x^2-5x+25\right)\)
A là đa thức bậc 1
=>A=x+5
=>B=x^2-5x+25
=>Chọn A
Câu 2. M có bậc 2 + 7 = 9
Chọn D
Câu 6. x³ + 125 = x³ + 5³ = (x + 5)(x² - 5x + 25)
Chọn A
a) Tìm được N = ( 10 x – 1 ) 2 nên x = 10 thì N = 99 2 = 9801.
b) Tìm được P = ( 5 c – d 2 ) 2 nên c = 5; d = 2 thì P = 21 2 = 441
a) \(x^2+10x=0\)
\(x\left(x+10\right)=0\)
\(\left[{}\begin{matrix}x=0\\x=-10\end{matrix}\right.\)
b) \(\left(x-7\right)^3=x-7\)
\(\left(x-7\right)^3-\left(x-7\right)=0\)
\(\left(x-7\right)\left[\left(x-7\right)^2-1\right]=0\)
\(\left(x-7\right)\left(x-7-1\right)\left(x-7+1\right)=0\)
\(\left(x-7\right)\left(x-8\right)\left(x-6\right)=0\)
\(\left[{}\begin{matrix}x=7\\x=8\\x=6\end{matrix}\right.\)
c) \(x^2-20x+100=0\)
\(x^2-10x-10x+100=0\)
\(x\left(x-10\right)-10\left(x-10\right)=0\)
\(\left(x-10\right)\left(x-10\right)=0\)
\(\left(x-10\right)^2=0\)
=> x = 10
a) \(x^2+10x=0\)
\(\Leftrightarrow x\left(x+10\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x+10=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=0\\x=-10\end{matrix}\right.\)
Vậy..
b) \(\left(x-7\right)^3=\left(x-7\right)\)
\(\Leftrightarrow\left(x-7\right)^3-\left(x-7\right)=0\)
\(\Leftrightarrow\left(x-7\right)\left[\left(x-7\right)^2-1\right]=0\)
\(\Leftrightarrow\left(x-7\right)\left(x-8\right)\left(x-6\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-7=0\\x-8=0\\x-6=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=7\\x=8\\x=6\end{matrix}\right.\)
Vậy..
c) \(x^2-20x+100=0\)
\(\Leftrightarrow\left(x-10\right)^2=0\)
\(\Rightarrow x-10=0\)
\(\Rightarrow x=10\)
\(C=16x^2-8x+2024\)
\(\Rightarrow C=16x^2-8x+1+2023\)
\(\Rightarrow C=\left(4x-1\right)^2+2023\ge2023\left(\left(4x-1\right)^2\ge0\right)\)
\(\Rightarrow Min\left(C\right)=2023\)
\(D=-25x^2+50x-2023\)
\(\Rightarrow D=-\left(25x^2-50x+25\right)-1998\)
\(\Rightarrow D=-\left(5x-5\right)^2-1998\le1998\left(-\left(5x-5\right)^2\le0\right)\)
\(\Rightarrow Max\left(D\right)=1998\)
\(B=-x^2+20x+100=-\left(x^2-20x+100\right)+200=-\left(x-10\right)^2+200\le200\left(-\left(x-10\right)^2\le0\right)\)
\(\Rightarrow Max\left(B\right)=200\)
\(E=\left(2x-1\right)^2-\left(3x+2\right)\left(x-5\right)\)
\(\Rightarrow E=4x^2-4x+1-\left(3x^2-13x-10\right)\)
\(\Rightarrow E=4x^2-4x+1-3x^2+13x+10\)
\(\Rightarrow E=x^2+9x+11=x^2+9x+\dfrac{81}{4}-\dfrac{81}{4}+11\)
\(\Rightarrow E=\left(x+\dfrac{9}{2}\right)^2-\dfrac{37}{4}\ge-\dfrac{37}{4}\left(\left(x+\dfrac{9}{2}\right)^2\ge0\right)\)
\(\Rightarrow Min\left(E\right)=-\dfrac{37}{4}\)
\(F=\left(3x-5\right)^2-\left(3x+2\right)\left(4x-1\right)\)
\(\Rightarrow F=9x^2-30x+25-\left(12x^2+3x-2\right)\)
\(\Rightarrow F=-3x^2-33x+27=-3\left(x^2-10x+9\right)\)
\(\Rightarrow F=-3\left(x^2-10x+25\right)+48=-3\left(x-5\right)^2+48\le48\left(-3\left(x-5\right)^2\le0\right)\)
\(\Rightarrow Max\left(F\right)=48\)
a) \(x^2-10\cdot2\cdot x+10^2=\left(x-10\right)^2\)
b) \(x^2+2\cdot5\cdot x+5^2=\left(x+5\right)^2\)
c) \(x^2-2\cdot6\cdot xy+\left(6y\right)^2=\left(x-6y\right)^2\)
đề của bạn là (x+10)2 à
Nếu đề là (x+10)2 thì đáp án là D nhé
nhớ like nha