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C = \(x^3\) + \(x^2\).y - 2\(x^2\) - \(xy\) - y\(^2\) + 3y + \(x\) - 1
C = (\(x^3\) + \(x^2\).y - 2\(x^2\)) - (\(xy\) + y\(^2\) - 2y) + (y + \(x\) - 2) + 1
C = \(x^2\).(\(x\) + y - 2) - y(\(x\) + y - 2) + (y + \(x\) - 2) + 1 (1)
Thay \(x+y-2\) vào biểu thức (1) ta có:
C = \(x^2\). 0 - y . 0 + 0 + 1
C = 0 - 0 + 0 + 1
C = 1
D = \(x\).(\(x^3\) - y)(\(x^3\) - 2y\(^2\))(\(x^3\) - 3y\(^2\))(\(x^3\) - 4y\(^4\)) (1)
Thay \(x\) = 2 và y = - 2 vào biểu thức (1) ta có:
D = 2.(2\(^3\)+2).(2\(^3\)- 2.(-2\()^2\)).(2\(^3\)-3(-2)\(^2\))(2\(^3\)- 4.(-2)\(^4\))
D = 2.(2\(^3\)+ 2).(8 - 8).(2\(^3\)- 3(-2)\(^2\))(2\(^3\)- 4.(-2)\(^4\))
D = 2.(2\(^3\)+ 2).0.(2\(^3\)- 3(-2)\(^2\))(2\(^3\)- 4.(-2)\(^4\))
D = 0
C = \(x^3\) + \(x^2\).y - 2\(x^2\) - \(xy\) - y\(^2\) + 3y + \(x\) - 1
C = (\(x^3\) + \(x^2\).y - 2\(x^2\)) - (\(xy\) + y\(^2\) - 2y) + (y + \(x\) - 2) + 1
C = \(x^2\).(\(x\) + y - 2) - y(\(x\) + y - 2) + (y + \(x\) - 2) + 1 (1)
Thay \(x+y-2\) vào biểu thức (1) ta có:
C = \(x^2\). 0 - y . 0 + 0 + 1
C = 0 - 0 + 0 + 1
C = 1
D = \(x\).(\(x^3\) - y)(\(x^3\) - 2y\(^2\))(\(x^3\) - 3y\(^2\))(\(x^3\) - 4y\(^4\)) (1)
Thay \(x\) = 2 và y = - 2 vào biểu thức (1) ta có:
D = 2.(2\(^3\)+2).(2\(^3\)- 2.(-2\()^2\)).(2\(^3\)-3(-2)\(^2\))(2\(^3\)- 4.(-2)\(^4\))
D = 2.(2\(^3\)+ 2).(8 - 8).(2\(^3\)- 3(-2)\(^2\))(2\(^3\)- 4.(-2)\(^4\))
D = 2.(2\(^3\)+ 2).0.(2\(^3\)- 3(-2)\(^2\))(2\(^3\)- 4.(-2)\(^4\))
D = 0
C = \(x^3\) + \(x^2\).y - 2\(x^2\) - \(xy\) - y\(^2\) + 3y + \(x\) - 1
C = (\(x^3\) + \(x^2\).y - 2\(x^2\)) - (\(xy\) + y\(^2\) - 2y) + (y + \(x\) - 2) + 1
C = \(x^2\).(\(x\) + y - 2) - y(\(x\) + y - 2) + (y + \(x\) - 2) + 1 (1)
Thay \(x+y-2\) vào biểu thức (1) ta có:
C = \(x^2\). 0 - y . 0 + 0 + 1
C = 0 - 0 + 0 + 1
C = 1
C = \(x^3\) + \(x^2\).y - 2\(x^2\) - \(xy\) - y\(^2\) + 3y + \(x\) - 1
C = (\(x^3\) + \(x^2\).y - 2\(x^2\)) - (\(xy\) + y\(^2\) - 2y) + (y + \(x\) - 2) + 1
C = \(x^2\).(\(x\) + y - 2) - y(\(x\) + y - 2) + (y + \(x\) - 2) + 1 (1)
Thay \(x+y-2\) vào biểu thức (1) ta có:
C = \(x^2\). 0 - y . 0 + 0 + 1
C = 0 - 0 + 0 + 1
C = 1
a/ \(C=\left(x^3+x^2y-2x^2\right)-\left(xy+y^2-2y\right)+\left(x+y-1\right)\)
\(C=x^2\left(x+y-2\right)-y\left(x+y-2\right)+\left(x+y-1\right)=x+y-1\) (do x+y-2=0)
Mà x+y-2=0 => x+y-1=1 => C=1
b/ Với x=2; y=2 Ta nhận thấy \(x^3-2y^2=2^3-2.2^2=2^3-2^3=0\) => D=0
\(M=x\left(x^2-y\right)\left(x^3-2y^2\right)\left(x^4-3y^3\right)\left(x^5-4y^4\right)\)
\(M=x\left(x^2-y\right)\left(2^3-2\left(-2\right)^2\right)\left(x^4-3y^3\right)\left(x^5-4y^4\right)\)
\(M=x\left(x^2-y\right)\left(8-2\cdot4\right)\left(x^4-3y^3\right)\left(x^5-4y^4\right)\)
\(M=x\left(x^2-y\right)\left(8-8\right)\left(x^4-3y^3\right)\left(x^5-4y^4\right)\)
\(M=x\left(x^2-y\right)\cdot0\cdot\left(x^4-3y^3\right)\left(x^5-4y^4\right)\)
⇒\(M=0\)
M=x(x2−y)(x3−2y2)(x4−3y3)(x5−4y4)M=x(x2−y)(x3−2y2)(x4−3y3)(x5−4y4)
M=x(x2−y)(23−2(−2)2)(x4−3y3)(x5−4y4)M=x(x2−y)(23−2(−2)2)(x4−3y3)(x5−4y4)
M=x(x2−y)(8−2⋅4)(x4−3y3)(x5−4y4)M=x(x2−y)(8−2⋅4)(x4−3y3)(x5−4y4)
M=x(x2−y)(8−8)(x4−3y3)(x5−4y4)M=x(x2−y)(8−8)(x4−3y3)(x5−4y4)
M=x(x2−y)⋅0⋅(x4−3y3)(x5−4y4)M=x(x2−y)⋅0⋅(x4−3y3)(x5−4y4)
⇒M=0M=0
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