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Ta có : \(M\left(x\right)=2x^3-3x^3+x^2-2x+1=-x^3+x^2-2x+1\)
\(N\left(x\right)=3x^4+4x^4-3x-1=7x^4-3x-1\)
a, \(M\left(x\right)+N\left(x\right)\)hay \(-x^3+x^2-2x+1+7x^4-3x-1=7x^4-x^3+x^2-5x\)
b, \(M\left(x\right)-N\left(x\right)\)hay \(-x^3+x^2-2x+1-7x^4+3x+1=-7x^4-x^3+x^2+x+2\)
Sửa đa thức M(x) = 3x4 - 2x3 + 5x2 - 4x + 1
\(P\left(x\right)=M\left(x\right)+N\left(x\right)\)
\(=3x^4-2x^3+5x^2-4x+1-3x^4+2x^3-3x^2+7x+5\)
\(=2x^2+3x+6\)
b, Tại x = -x
< = > 2x = 0 <=> x = 0 thì giá trị của biểu thức P ( x ) = 6
a, M(\(x\) )+N(\(x\)) = 3\(x^4\) - 2\(x\)3 + 5\(x^2\) - \(4x\)+ 1 + ( -3\(x^4\) + 2\(x^3\)- 3\(x^2\)+ 7\(x\) + 5)
M(\(x\)) + N(\(x\)) = ( 3\(x^4\)- 3\(x^4\))+( -2\(x^3\) + 2\(x^3\))+(5\(x^2\) - 3\(x^2\))+( 7\(x-4x\)) +(1+5)
M(\(x\)) + N(\(x\)) = 0 + 0 + 2\(x^2\) + 3\(x\) + 6
M(\(x\)) + N(\(x\)) = 2\(x^2\) + 3\(x\) + 6
b, P(\(x\)) = M(\(x\)) + N(\(x\)) = 2\(x^2\) + 3\(x\) + 6
P(-2) = 2.(-2)2 + 3.(-2) + 6 = 8 - 6 + 6 = 8
a. M(x) + N(x) = 3x3 - 3x + x2 + 5 + 2x2 - x + 3x3 + 9
= (3x3 + 3x3) + ( x2 + 2x2 ) + ( -3x - x ) + (5 + 9)
= 6x3 + 3x2 - 4x + 14
b. M(x) + N(x) - P(x) = 6x3 + 3x2 + 2x
=> 6x3 + 3x2 - 4x + 14 - P(x) = 6x3 + 3x2 + 2x
=> 6x3 + 3x2 - 4x + 14 - ( 6x3 + 3x2 + 2x) = P(x)
=> 6x3 + 3x2 - 4x + 14 - 6x3 - 3x2 - 2x = P(x)
=> (6x3 - 6x3 ) + (3x2 - 3x2 ) + (-4x - 2x ) + 14 = P(x)
=> -6x + 14 = P(x)
Ta có : -6x + 14 = 0
=> -6x = -14
=> x = 7/3
=> Đa thức P(x) = -6x + 14 có nghiệm là 7/3
=>
a) Ta có: \(A=\left(-\dfrac{1}{3}x^2y^4\right)\cdot\left(-\dfrac{3}{5}x^3y\right)^2\)
\(=\dfrac{-1}{3}x^2y^4\cdot\dfrac{-9}{5}x^6y^2\)
\(=\left(\dfrac{-1}{3}\cdot\dfrac{-9}{5}\right)\cdot\left(x^2\cdot x^6\right)\cdot\left(y^4\cdot y^2\right)\)
\(=\dfrac{3}{5}x^8y^6\)
\(a;M\left(x\right)+N\left(x\right)=\left(2x^3-5x^2+x-2\right)+\left(-3x^3+5x^2-x+1\right)\)
\(=2x^3-5x^2+x-2-3x^3+5x^2-x+1\)
\(=-x^3-1\)
\(b;M\left(x\right)-N\left(x\right)=\left(2x^3-5x^2+x^2-2\right)-\left(-3x^3+5x^2-x+1\right)\)
\(=2x^3-5x^2+x-2+3x^3-5x^2+x-1\)
\(=5x^3-10x^2+2x-3\)
\(c;3N\left(x\right)-2M\left(x\right)=3\left(2x^3-5x^2+x-2\right)-2\left(-3x^3+5x^2-x+1\right)\)
\(=6x^3-15x^2+3x-6+6x^3-10x^2+2x-2\)
\(=12x^3-25x^2+5x-8\)
a) N=-2x2+3xy+3x2-3y-1
=-2x2+3x2+3xy-3y-1
=x2+3xy-3y-1
=>M+N=(x2+2xy+y-1)+(x2+3xy-3y-1)
=x2+2xy+y-1+x2+3xy+-3y-1
=x2+x2+2xy+3xy+y-3y-1-1
=2x2+5xy-2y-2
b)M-N= (x2+2xy+y-1)-(x2+3xy-3y-1)
=x2+2xy+y-1-x2-3xy+3y+1
=x2-x2+2xy-3xy+y+3y-1+1
=-xy+4y
M+N= (x2-3x+1)+(-x2-2x-1)
=x2-3x+1-x2-2x-1
=x2-x2-3x-2x+1-1
=-5x
M-N=(x2-3x+1)-(-x2-2x-1)
=x2-3x+1+x2+2x+1
=x2+x2-3x+2x+1+1
=2x2-x+2