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\(\left(3-x\right)^{10x}:\left(3-x\right)^{20}=1\)
=>\(\left(3-x\right)^{10x-20}=1\)
=>10x-20=0 hoặc 3-x=1
=>x=2 hoặc x=2
=>x=2
\(P\left(x\right)=2x^4-3x^2+x-\dfrac{2}{3}\)
\(Q\left(x\right)=x^4-x^3+x^2+\dfrac{5}{3}\)
a) \(P\left(x\right)+Q\left(x\right)=2x^4-3x^2+x-\dfrac{2}{3}+x^4-x^3+x^2+\dfrac{5}{3}\)
\(\Rightarrow P\left(x\right)+Q\left(x\right)=3x^4-x^3-2x^2+x-\dfrac{2}{3}+\dfrac{5}{3}\)
\(\Rightarrow P\left(x\right)+Q\left(x\right)=3x^4-x^3-2x^2+x+1\)
b) \(P\left(x\right)-Q\left(x\right)=2x^4-3x^2+x-\dfrac{2}{3}-\left(x^4-x^3+x^2+\dfrac{5}{3}\right)\)
\(\Rightarrow P\left(x\right)-Q\left(x\right)=2x^4-3x^2+x-\dfrac{2}{3}-x^4+x^3-x^2-\dfrac{5}{3}\)
\(\Rightarrow P\left(x\right)-Q\left(x\right)=x^4+x^3-4x^2+x-\dfrac{2}{3}-\dfrac{5}{3}\)
\(\Rightarrow P\left(x\right)-Q\left(x\right)=x^4+x^3-4x^2+x-\dfrac{7}{3}\)
a) P(x) + Q(x) = (2x⁴ - 3x² + x - 2/3) + (x⁴ - x³ + x² + 5/3)
= 2x⁴ - 3x² + x - 2/3 + x⁴ - x³ + x² + 5/3
= (2x⁴ + x⁴) - x³ + (-3x² + x²) + x + (-2/3 + 5/3)
= 3x⁴ - x³ - 2x² + x + 1
b) P(x) - Q(x) = (2x⁴ - 3x² + x - 2/3) - (x⁴ - x³ + x² + 5/3)
= 2x⁴ - 3x² + x - 2/3 - x⁴ + x³ - x² - 5/3
= (2x⁴ - x⁴) + x³ + (-3x² - x²) + x + (-2/3 - 5/3)
= x⁴ + x³ - 4x² + x - 7/3
a)\(M\left(x\right)=x^4-2x^3+x^2-5x+1\)
\(N\left(x\right)=8x^4-5x^3+x^2-3\)
a. M(x) = x2 -5x -2x3 + x4 + 1
= x4 - 2x3 + x2 - 5x + 1
N(x) = -5x3 -3 + 8x4 + x2
= 8x4 - 5x3 + x2 - 3
b. M(x) + N(x) = x4 - 2x3 + x2 - 5x + 1 + 8x4 - 5x3 + x2 - 3
= (x4 + 8x4) + (-2x3 - 5x3) + (x2 + x2 ) - 5x + (1 - 3)
= 9x4 - 7x3 + 2x2 - 5x - 2
M (x) - N (x) = x4 - 2x3 + x2 - 5x + 1 - ( 8x4 - 5x3 + x2 - 3)
= x4 - 2x3 + x2 - 5x + 1 - 8x4 + 5x3 - x2 + 3
= (x4 - 8x4 ) + ( -2x3 + 5x3 ) + (x2 - x2 ) - 5x + (1 + 3)
= -7x4 + 3x3 - 5x + 4
B(3)=2*3^2-4*3+3=18-12+3=9
B(-1/2)=2*1/4-4*(-1/2)+3=1/2+3+2=1/2+5=11/2
\(\begin{array}{l}a)5{x^3} + {x^3} = (5 + 1){x^3} = 6{x^3}\\b)\dfrac{7}{4}{x^5} - \dfrac{3}{4}{x^5} = \left( {\dfrac{7}{4} - \dfrac{3}{4}} \right){x^5} = \dfrac{4}{4}{x^5} = {x^5}\\c)( - 0,25{x^2}).(8{x^3}) = ( - 0,25.8).({x^2}.{x^3}) = - 2.{x^5}\end{array}\)
`@` `\text {Ans}`
`\downarrow`
`a,`
`M(x) = P(x) + Q(x)`
`= 2x^4 -3x^2 + x -2/3 + x^4 - x^3 + x^2 +5/3 `
`= (2x^4 + x^4) - x^3 + (-3x^2 + x^2) + x + (-2/3 + 5/3)`
`= 3x^4 - x^3 - 2x^2 + x + 1`
`b,`
`N(x) = P(x) - Q(x)`
`= 2x^4 -3x^2 + x -2/3 - (x^4 - x^3 + x^2 +5/3)`
`= 2x^4 -3x^2 + x -2/3 - x^4 + x^3 - x^2 -5/3`
`= (2x^4 - x^4) + x^3 + (-3x^2 - x^2) + x + (-2/3 - 5/3)`
`= x^4 + x^3 - 4x^2 + x - 7/3`
Bậc của đa thức: `4.`
(3-x)3=3-x
khi và chỉ khi 3-x=0 hoặc 3-x=1
suy ra x=3; x=2