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a, P(x)=\(3x^3+2x^2-2x+7-x^2-x\)
=\(3x^3+\left(2x^2-x^2\right)+\left(-2x-x\right)+7\)
=\(3x^3+x^2-3x+7\)
Q(x)=\(-3x^3+x-14-2x-x^2-1\)
= -3x\(^3\)+\((x-2x)\)+(-14-1)-x\(^2\)
= -3x\(^3\)-x -15 -x\(^2\)
b, M(x)=P(x)+Q(x)=\((3x^3+x^2-3x+7)\)+ (-3x\(^3\)-x-15-x\(^2\))
=\(3x^3+x^2-3x+7\) -3x\(^3\) -x -15 -x\(^2\)
=(3x\(^3\)- 3x\(^3\)) + (x\(^2\)-x\(^2\)) + (-3x-x) + (7-15)
= -4x - 8
a, P(x)=3x3+2x2−2x+7−x2−x3x3+2x2−2x+7−x2−x
=3x3+(2x2−x2)+(−2x−x)+73x3+(2x2−x2)+(−2x−x)+7
=3x3+x2−3x+73x3+x2−3x+7
Q(x)=−3x3+x−14−2x−x2−1−3x3+x−14−2x−x2−1
= -3x33+(x−2x)(x−2x)+(-14-1)-x22
= -3x33-x -15 -x22
b, M(x)=P(x)+Q(x)=(3x3+x2−3x+7)(3x3+x2−3x+7)+ (-3x33-x-15-x22)
=3x3+x2−3x+73x3+x2−3x+7 -3x33 -x -15 -x22
=(3x3- 3x3) + (x2-x2) + (-3x-x) + (7-15)
= -4x - 8
a) P(x)=5x3 - 3x - x + 7
Q(x)=-5x3- x2 + 2x + 2x -3 - 2
b) P(x) + Q(x) = ( 5x3- 3x - x + 7)+ ( -5x3- x2 + 2x + 2x - 3 - 2 )
=5x3 - 3x - x + 7 - 5x3 - x2 + 2x + 2x - 3 - 2
=(5x3-5x3)+(-x2)+(-3x-x+2x+2x)+(7-3-2)
=> M = -x2+2
P(x)-Q(x)= (5x3-3x-x+7)-(-5x3-x2+2x+2x-3-2)
= 5x3-3x-x+7+5x3-x2+2x+2x-3-2
=(5x3+5x3)+(-x2)+(-3x-x+2x+2x)+(7-3-2)
=> N =10x3 -x2 +2
c)-x2+2=0
-x2=0+2
-x2=2
=>-x2=\(-\sqrt{2}\)
P(x) = 5x3 - 3x + 7 - x = 5x3 + ( -3x - x ) + 7 = 5x3 - 4x + 7
Q(x) = -5x3 + 2x - 3 + 2x - x2 - 2 = -5x3 + ( 2x + 2x ) - x2 + ( -3 - 2 ) = -5x3 + 4x - x2 - 5
M(x) = P(x) + Q(x)
= 5x3 - 4x + 7 + ( -5x3 + 4x - x2 - 5 )
= ( 5x3 - 5x3 ) + ( 4x - 4x ) - x2 + ( 7 - 5 )
= -x2 + 2
N(x) = P(x) - Q(x)
= ( 5x3 - 4x + 7 ) - ( -5x3 + 4x - x2 - 5 )
= 5x3 - 4x + 7 + 5x3 - 4x + x2 + 5
= ( 5x3 + 5x3 ) + ( -4x - 4x ) + x2 + ( 7 + 5 )
= 10x3 - 8x + x2 + 12
M(x) = 0 <=> -x2 + 2 = 0
<=> -x2 = -2
<=> x2 = 2
<=> x = \(\pm\sqrt{2}\)
Vậy nghiệm của M(x) là \(\pm\sqrt{2}\)
a,P(x)=4x\(^3\)+2x\(^2\)-2x+7-x\(^2\)-x
=4x\(^3\)+(2x\(^2\)-x\(^2\))+(-2x-x)+7
=4x\(^3\)+x\(^2\)-3x+7
Q(x)=-4x\(^3\)+x-14-2x-x\(^2\)-1
=-4x\(^3\)-x\(^2\)+(x-2x)+(-14-1)
= -4x\(^3\)-x\(^2\) -x -15
b, P(x)+Q(x)=4x\(^3\)+x\(^2\)-3x+7-4x\(^3\)-x\(^2\) -x -15
=\(\left(4x^3-4x^3\right)\)+\(\left(x^2-x^2\right)\)+(-3x-x)+(7-15)
= -4x-8
P(x)-Q(x)=(4x\(^3\)+x\(^2\)-3x+7)-(-4x\(^3\)-x\(^2\) -x -15)
=4x\(^3\)+x\(^2\)-3x+7+4x\(^3\)+x\(^2\) +x +15
=\(\left(4x^3+4x^3\right)\)+\(\left(x^2+x^2\right)\)+(-3x+x)+(7+15)
= \(8x^3\) + \(2x^2\) - 2x + 22
Nhìn tưởng đề sai ... nhưng nó có sai đâu :v
a, Ta có :
\(P\left(x\right)=5x^3-3x+2-x-x^2+\frac{3}{5}x+3=5x^3-\frac{17}{5}x+5-x^2\)
\(Q\left(x\right)=-5x^3+2x-3+2x-x^2-2=-5x^3+4x-5-x^2\)
b, Ta có :
\(M\left(x\right)=5x^3-\frac{17}{5}x+5-x^2-5x^3+4x-5-x^2=\frac{3}{5}x-2x^2\)
Tương tự vs N(x)
c, Ta có : \(M\left(x\right)=\frac{3}{5}x-2x^2=0\)
\(\Leftrightarrow x\left(\frac{3}{5}-2x\right)=0\Leftrightarrow\orbr{\begin{cases}x=0\\2x=\frac{3}{5}\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=\frac{3}{10}\end{cases}}}\)
a,P(x) = 5x3-x2-3x+7
Q(x)=-3x3 -x2-x-1
b, M(x)= P(x)+Q(x)= 5x3-x2-3x+7+-3x3 -x2-x-1=2x3-2x2-4x+6
\N(x)=P(x)-Q(x)= 5x3-x2-3x+7-(-3x3 -x2-x-1)= 8X3-2x+8
c,P(x)=-Q(x)
5x3-x2-3x+7=-(-3x3 -x2-x-1)
2x3-2x2-4x+6=0
đề có vẻ hơi sai sai mếu k thì nghiệm là căn thức phức tạp ??
cô mình còn bắt tìm cả x cơ bạn ạ