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\(Fe+2HCl\rightarrow FeCl_2+H_2\)
\(2Al+3H_2SO_4\rightarrow Al_2\left(SO_4\right)_3+3H_2\)
\(CuO+H_2SO_4\rightarrow CuSO_4+H_2O\)
\(2Al\left(OH\right)_3+3H_2SO_4\rightarrow Al_2\left(SO_4\right)_3+6H_2O\)
\(CuO+2HNO_3\rightarrow Cu\left(NO_3\right)_2+H_2O\)
1. Fe + 2HCl → FeCl2 + H2
2Al + 3H2SO4 → Al2(SO4)3 + 3H2
CuO + H2SO4 → CuSO4 + H2O
2Al(OH)3 + 3H2SO4 → Al2(SO4)3 + 6H2O
CuO + 2HNO3 → Cu(NO3)2 + H2O
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phân tích đa thức thành phân tử nha quên mất không ghi đề =))
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\(C=16x^2-8x+2024\)
\(\Rightarrow C=16x^2-8x+1+2023\)
\(\Rightarrow C=\left(4x-1\right)^2+2023\ge2023\left(\left(4x-1\right)^2\ge0\right)\)
\(\Rightarrow Min\left(C\right)=2023\)
\(D=-25x^2+50x-2023\)
\(\Rightarrow D=-\left(25x^2-50x+25\right)-1998\)
\(\Rightarrow D=-\left(5x-5\right)^2-1998\le1998\left(-\left(5x-5\right)^2\le0\right)\)
\(\Rightarrow Max\left(D\right)=1998\)
\(B=-x^2+20x+100=-\left(x^2-20x+100\right)+200=-\left(x-10\right)^2+200\le200\left(-\left(x-10\right)^2\le0\right)\)
\(\Rightarrow Max\left(B\right)=200\)
\(E=\left(2x-1\right)^2-\left(3x+2\right)\left(x-5\right)\)
\(\Rightarrow E=4x^2-4x+1-\left(3x^2-13x-10\right)\)
\(\Rightarrow E=4x^2-4x+1-3x^2+13x+10\)
\(\Rightarrow E=x^2+9x+11=x^2+9x+\dfrac{81}{4}-\dfrac{81}{4}+11\)
\(\Rightarrow E=\left(x+\dfrac{9}{2}\right)^2-\dfrac{37}{4}\ge-\dfrac{37}{4}\left(\left(x+\dfrac{9}{2}\right)^2\ge0\right)\)
\(\Rightarrow Min\left(E\right)=-\dfrac{37}{4}\)
\(F=\left(3x-5\right)^2-\left(3x+2\right)\left(4x-1\right)\)
\(\Rightarrow F=9x^2-30x+25-\left(12x^2+3x-2\right)\)
\(\Rightarrow F=-3x^2-33x+27=-3\left(x^2-10x+9\right)\)
\(\Rightarrow F=-3\left(x^2-10x+25\right)+48=-3\left(x-5\right)^2+48\le48\left(-3\left(x-5\right)^2\le0\right)\)
\(\Rightarrow Max\left(F\right)=48\)
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Phân tích đa thức:
x^4 + 2x^3 - x^2 - 2x + 1
= (x^4 + 2x^3) - (x^2 + 2x) + 1
= x^3(x + 2) - x(x + 2) + 1
= (x^3 - x)(x + 2) + 1
= x(x^2 - 1)(x + 2) + 1
= x(x - 1)(x + 1)(x + 2) + 1
Vậy phương trình đã cho có các nghiệm là x = -2, x = -1, x = 0 và x = 1.
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(x + 2y)² - (x - y)²
= (x + 2y - x + y)(x + 2y + x - y)
= 3y(2x + y)
\(\left(x+2y\right)^2-\left(x-y\right)^2\)
\(=\left[\left(x+2y\right)-\left(x-y\right)\right]\left[\left(x+2y\right)+\left(x-y\right)\right]\)
\(=\left(x+2y-x+y\right)\left(x+2y+x-y\right)\)
\(=3y\left(2x+y\right)\)