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a) x4 - 10x3 - 15x2 + 20x + 4
= x4 + 2x3 - 12x3 - 24x2 + 9x2 + 18x + 2x + 4
= x3(x + 2) - 12x2(x + 2) + 9x(x + 2) + 2(x + 2)
= (x + 2)(x3 - 12x2 + 9x + 2)
b)
2x4 - 5x3 - 27x2 + 25x + 50
= 2x3(x - 2) - x2(x - 2) - 25x(x - 2) - 25(x - 2)
= (x - 2)(2x3 - x2 - 25x - 25)
c)\(3x^4+6x^3-33x^2-24x+48\)
\(=3\left(x^4+2x^3-11x^2-8x+16\right)\)
\(=3\left(x^4-x^3-4x^2+3x^3-3x^2-12x-4x^2+4x+16\right)\)
\(=3\left(x^2\left(x^2-x-4\right)+3x\left(x^2-x-4\right)-4\left(x^2-x-4\right)\right)\)
\(=3\left(x^2+3x-4\right)\left(x^2-x-4\right)\)
\(=3\left(x^2-x+4x-4\right)\left(x^2-x-4\right)\)
\(=3\left[x\left(x-1\right)+4\left(x-1\right)\right]\left(x^2-x-4\right)\)
\(=3\left(x-1\right)\left(x+4\right)\left(x^2-x-4\right)\)
(1) cho A = 4,25 x(b + 41,53 ) - 125. tim b de A co gia tri =300 . (2)
\(\dfrac{2x-1}{\left(x-2\right)^2}+\dfrac{5x}{x-2}-\dfrac{25x}{5\left(x-2\right)}=0\)
\(\Leftrightarrow\dfrac{\left(2x-1\right).5}{\left(x-2\right)^2.5}+\dfrac{5x\left(x-2\right).5}{\left(x-2\right).\left(x-2\right).5}-\dfrac{25x\left(x-2\right)}{5\left(x-2\right)\left(x-2\right)}=0\)
\(\Leftrightarrow\dfrac{10x-5+25x^2-50x-25x^2+50x}{5\left(x-2\right)^2}=0\)
\(\Leftrightarrow\dfrac{10x-5}{5\left(x-2\right)^2}=0\)
\(\Leftrightarrow\dfrac{5\left(2x-1\right)}{5\left(x-2\right)^2}=0\)
\(\Leftrightarrow\dfrac{2x-1}{x-2}=0\)
\(\Leftrightarrow x=\dfrac{1}{2}\)
\(\frac{4}{-25x^2+20x-3}=\frac{3}{5x-1}-\frac{2}{5x-3}\) ( ĐKXĐ : \(x\ne\frac{3}{5};x\ne\frac{1}{5}\) )
\(\Leftrightarrow\frac{-4}{\left(5x-3\right)\left(5x-1\right)}=\frac{3\left(5x-3\right)}{\left(5x-3\right)\left(5x-1\right)}-\frac{2\left(5x-1\right)}{\left(5x-3\right)\left(5x-1\right)}\)
\(\Leftrightarrow-4=-15x-9-10x+2\)
\(\Leftrightarrow5x=3\)
\(\Leftrightarrow x=\frac{3}{5}\) ( loại )
Vậy phương trình trên vô nghiệm
\(2x^4-5x^3-27x^2+25x+50=0\)
\(\Leftrightarrow2x^4-4x^3-x^3+2x^2-25x^2+50x+25x^2-25x+50=0\)
\(\Leftrightarrow2x^3\left(x-2\right)-x^2\left(x-2\right)-25x\left(x-5\right)+25\left(x+5\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(2x^3-x^2-25x+25\right)=0\)
:D sorry mk ko bt phân tích 2x^3-x^2-25x+25 :D
chịu