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M (x)- N (x)
= \(3x^4+5x^3-3x^2+4x-2\) - \(2x^4-5x^3+4x^2-4x+5\)
= \(x^4+x^2+3\)
Do \(x^4\ge0\) ( với mọi x )
\(x^2\ge0\) ( với mọi x )
=> \(x^4+x^2+3>0\) ( với mọi x )
Vậy M(x) - N(x) vô nghiệm
a) M+N+P= 3x3-4x2-x+5+x3-2x2+5x-4+3x3-x2-5x+10
=3x3+x3+3x3-4x2-2x2-x2-x+5x-5x+5-4+10
=7x3-7x2-x+11
b)M-N-P=3x3-4x2-x+5-(x3-2x2+5x-4)-(3x3-x2-5x+10)
=3x3-4x2-x+5-x3+2x2-5x+4-3x3+x2+5x-10
=3x3-x3-3x3-4x2+2x2+x2-x-5x+5x+5+4-10
=-x3-x2-x-1
c)N-M-P=x3-2x2+5x-4-(3x3-4x2-x+5)-(3x3-x2-5x+10)
=x3-2x2+5x-4-3x3+4x2+x-5-3x3+x2+5x-10
=x3-3x3-3x3-2x2+4x2+x2+5x+x+5x-4-5-10
=-5x3+3x2+11x-19
d)P-N-M=3x3-x2-5x+10-(x3-2x2+5x-4)-(3x3-4x2-x+5)
=3x3-x2-5x+10-x3+2x2-5x+4-3x3+4x2+x-5
=3x3-x3-3x3-x2+2x2+4x2-5x-5x+x+10+4-5
=-x3+5x2-9x+9
Bài 1:
a)
\(F+G+H=(x^3-2x^2+3x+1)+(x^3+x-1)+(2x^2-1)\)
\(=2x^3+4x-1\)
b)
\(F-G+H=0\)
\(\Leftrightarrow (x^3-2x^2+3x+1)-(x^3+x-1)+(2x^2-1)=0\)
\(\Leftrightarrow 2x+1=0\)
\(\Leftrightarrow x=-\frac{1}{2}\)
Bài 2:
a)
\(A=-4x^5-x^3+4x^2-5x+9+4x^5-6x^2-2\)
\(=(-4x^5+4x^5)-x^3+(4x^2-6x^2)-5x+(9-2)\)
\(=-x^3-2x^2-5x+7\)
\(B=-3x^4-2x^3+10x^2-8x+5x^3\)
\(=-3x^4+(5x^3-2x^3)+10x^2-8x\)
\(=-3x^4+3x^3+10x^2-8x\)
b)
\(P=A+B=(-x^3-2x^2-5x+7)+(-3x^4+3x^3+10x^2-8x)\)
\(=-3x^4+(3x^3-x^3)+(10x^2-2x^2)-(8x+5x)+7\)
\(=-3x^4+2x^3+8x^2-13x+7\)
\(P(-1)=-3.(-1)^4+2(-1)^3+8(-1)^2-12(-1)+7=23\)
\(Q=A-B=(-x^3-2x^2-5x+7)-(-3x^4+3x^3+10x^2-8x)\)
\(=3x^4-(x^3+3x^3)-(2x^2+10x^2)+(8x-5x)+7\)
\(=3x^4-4x^3-12x^2+3x+7\)
a ) M(x) + N(x) + P(x) = (\(3x^3+x^2+4x^4-x-3x^3+5x^4+x^2-6\)) + (\(-x^2-x^4+4x^3-x^2-5x^3+3x+1+x\)) + (\(1+2x^5-3x^2+x^5+3x^3-x^4-2x\))
= \(3x^3+x^2+4x^4-x-3x^3+5x^4+x^2-6\) \(-x^2-x^4+4x^3-x^2-5x^3+3x+1+x\)\(1+2x^5-3x^2+x^5+3x^3-x^4-2x\)
= ( \(3x^3-3x^3+4x^3-5x^3+3x^3\) ) + ( \(x^2+x^2-x^2-x^2-3x^2\) ) + (\(4x^4+5x^4-x^4-x^4\) ) + ( \(-x+3x+x-2x\) ) + ( \(-6+1+1\) ) + (\(2x^5+x^5\) )
= \(2x^3-3x^2+7x^4+x-4+3x^5\)
a) M+N-P= (5x4-4x3-3x2-2x+4)+(x4-3x2+5x-7)-(-2x4-5x3+2x2-x-9)
=5x4-4x3-3x2-2x+4+x4-3x2+5x-7-2x4+5x3-2x2+x+9
=5x4+x4-2x4-4x3+5x3-3x2-3x2-2x2-2x+5x+x+4-7+9
=4x4+x3-8x2+4x+6
b) M-N+P=(5x4-4x3-3x2-2x+4)-(x4-3x2+5x-7)+(-2x4-5x3+2x2-x-9)
=5x4-4x3-3x2-2x+4-x4+3x2-5x+7+-2x4-5x3+2x2-x-9
=5x4-x4-2x4-4x3-5x3-3x2+3x2+2x2-2x-5x-x+4+7-9
=2x4-9x3+2x2-8x+2
c)N-M-P=(x4-3x2+5x-7)-(5x4-4x3-3x2-2x+4)-(-2x4-5x3+2x2-x-9)
=x4-3x2+5x-7-5x4+4x3+3x2+2x-4-2x4+5x3-2x2+x+9
=x4-5x4-2x4+4x3+5x3-3x2+3x2-2x2+5x+2x+x-7-4+9
=-6x4+9x3-2x2+8x-2
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