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R(x) = 2x2 + 3x - 1
- M(x) = -x3 + x2
x3 + x2 + 3x - 1
Vậy R(x) - M(x) = x3 + x2 + 3x - 1
a. Kiểm tra lại mẫu số vế phải, \(7-5x\) hay \(7-3x\)
b. ĐKXĐ: \(x\ne-\dfrac{5}{3}\)
\(\dfrac{3x+5}{12}=\dfrac{3}{5+3x}\)
\(\Leftrightarrow\dfrac{\left(3x+5\right)^2}{12\left(3x+5\right)}=\dfrac{36}{12\left(3x+5\right)}\)
\(\Rightarrow\left(3x+5\right)^2=36=6^2\)
\(\Rightarrow\left[{}\begin{matrix}3x+5=6\\3x+5=-6\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=-\dfrac{11}{3}\end{matrix}\right.\) (thỏa mãn)
* Trả lời:
\(\left(1\right)\) \(-3\left(1-2x\right)-4\left(1+3x\right)=-5x+5\)
\(\Leftrightarrow-3+6x-4-12x=-5x+5\)
\(\Leftrightarrow6x-12x+5x=3+4+5\)
\(\Leftrightarrow x=12\)
\(\left(2\right)\) \(3\left(2x-5\right)-6\left(1-4x\right)=-3x+7\)
\(\Leftrightarrow6x-15-6+24x=-3x+7\)
\(\Leftrightarrow6x+24x+3x=15+6+7\)
\(\Leftrightarrow33x=28\)
\(\Leftrightarrow x=\dfrac{28}{33}\)
\(\left(3\right)\) \(\left(1-3x\right)-2\left(3x-6\right)=-4x-5\)
\(\Leftrightarrow1-3x-6x+12=-4x-5\)
\(\Leftrightarrow-3x-6x+4x=-1-12-5\)
\(\Leftrightarrow-5x=-18\)
\(\Leftrightarrow x=\dfrac{18}{5}\)
\(\left(4\right)\) \(x\left(4x-3\right)-2x\left(2x-1\right)=5x-7\)
\(\Leftrightarrow4x^2-3x-4x^2+2x=5x-7\)
\(\Leftrightarrow-x-5x=-7\)
\(\Leftrightarrow-6x=-7\)
\(\Leftrightarrow x=\dfrac{7}{6}\)
\(\left(5\right)\) \(3x\left(2x-1\right)-6x\left(x+2\right)=-3x+4\)
\(\Leftrightarrow6x^2-3x-6x^2-12x=-3x+4\)
\(\Leftrightarrow-15x+3x=4\)
\(\Leftrightarrow-12x=4\)
\(\Leftrightarrow x=-\dfrac{1}{3}\)
\(Q=x^2+2xy+\left(-3x^3+3x^3\right)+\left(2y^3-y^3\right)=x^2+2xy+y^3\)
\(P=\left(\dfrac{1}{3}x^2y-\dfrac{1}{3}x^2y\right)+\left(xy^2+\dfrac{1}{2}xy^2\right)-\left(xy+5xy\right)=\dfrac{3}{2}xy^2-6xy\)
Đặt `3(x+2)-1/3(6-3x)=0`
`<=>3(x+2)-(2-x)=0`
`<=>3x+2+x-2=0`
`<=>4x=0`
`<=>x=0`
Vậy nghiệm của đa thức là 0
`3x(x-5)-(x+3x)=0`
`<=>3x(x-5)-4x=0`
`<=>x(3x-15-4)=0`
`<=>x(3x-19)=0`
`<=>[(x=0),(3x-19=0):}`
`<=>[(x=0),(x=19/3):}`
Vậy nghiệm đa thức là 0 và `19/3`.
a) Đặt \(3\left(x+2\right)-\dfrac{1}{3}\left(6-3x\right)=0\)
\(\Leftrightarrow3x+6-2+x=0\)
\(\Leftrightarrow4x=-4\)
hay x=-1
b) Đặt 3x(x-5)-(x+3x)=0
\(\Leftrightarrow3x^2-15x-4x=0\)
\(\Leftrightarrow x\left(3x-19\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{19}{3}\end{matrix}\right.\)
`1)` Yêu cầu là gì ạ?
`2)`
`P(x)-Q(x)=`\((6x^3-3x^2+5x-1)-(-6x^3+3x^2-2x+7)\)
`= 6x^3-3x^2+5x-1+6x^3-3x^2+2x-7`
`= (6x^3+6x^3)+(-3x^2-3x^2)+(5x+2x)+(-1-7)`
`= 12x^3-6x^2+7x-8`
`3)`
`(-3x^3+15x^2+81x):(-3x)`
`= (-3x^3) \div (-3x) + 15x^2 \div (-3x) + 81x \div (-3x)`
`= x^2-5x-27`
`@` `\text {Ans}`
`\downarrow`
`a,`
`P(x)+Q(x) = (3x^4-2x^3+3x+11)+(3x^2- x^3-5x+3x+4-x+2x^4)`
`= 3x^4-2x^3+3x+11+3x^2- x^3-5x+3x+4-x+2x^4`
`= (3x^4 + 2x^4) + (-2x^3 - x^3) + 3x^2 + (3x + 3x - 5x - x) + (11+4)`
`= 5x^4 - 3x^3 + 3x^2 + 15`
`b,`
` A(x) = P(x) + B(x)`
Thay `B(x) = 2x^3 - 3x^4 - 2`
`A(x) = P(x) + B (x)`
`=> A (x) = (2x^3 - 3x^4 - 2)+(3x^4 - 2x^3 + 3x + 11)`
`= 2x^3 - 3x^4 - 2+ 3x^4 - 2x^3 + 3x + 11`
`= (2x^3 - 2x^3) + (-3x^4 + 3x^4) + 3x + (-2+11) `
`= 3x + 9`
`A(x) = 3x+9 = 0`
`=> 3x = 0-9`
`=> 3x = -9`
`=> x = -9 \div 3`
`=> x = -3`
Vậy, nghiệm của đa thức là `x = -3.`