a,P(x)=(x\(\(^3\)\)+x\(\(^3\)\))+(-2x-x)+1=2x\(\(^3\)\)-3x +1
Sắp xếp: Như trên
Q(x)=2x\(\(^2\)\)+(-8-7)+(-4x+x)+2x\(\(^3\)\)=2x\(\(^2\)\)-15-3x+2x\(\(^3\)\)
Sắp xếp: 2x\(\(^3\)\)+2x\(\(^2\)\)-3x-15
b, Mình tính luôn kết quả nha bn. P(x)+Q(x)=4x\(\(^3\)\)+2x\(\(^2\)\)-6x-14
c,A(x)=-2x\(\(^2\)\)+16
d,B(x)= 2x\(\(^2\)\)-16
e, A(x)=-2x\(\(^2\)\)+16 =0 => -2x\(\(^2\)\)=-16 => x\(\(^2\)\)=8 => x=\(\(\sqrt{8}\)\)
d, B(x)=2x\(\(^2\)\)-16=0 => 2x\(\(^2\)\)=16 => x\(\(^2\)\)=8 => x=\(\(\sqrt{8\ }\)\)
a) Thu gọn, sắp xếp.
\(P\left(x\right)=x^3-2x+x^3-x+1.\)
\(=\left(x^3+x^3\right)+\left(-2x-x\right)+1\)
\(=2x^3-3x+1\)
\(Q\left(x\right)=2x^2-8-4x+2x^3+x-7\)
\(=2x^3+2x^2+\left(-4x+x\right)+\left(-8-7\right)\)
\(=2x^3+2x^2-3x-15\)
b) Tính \(P\left(x\right)+Q\left(x\right)=\left(2x^3-3x+1\right)+\left(2x^3+2x^2-3x-15\right)\)
\(=2x^3-3x+1+2x^3+2x^2-3x-15\)
\(=\left(2x^3+2x^3\right)+2x^2+\left(-3x-3x\right)+\left(1-15\right)\)
\(=4x^3+2x^2-6x-14\)
b) \(A\left(x\right)=P\left(x\right)-Q\left(x\right)=\left(2x^3-3x+1\right)-\left(2x^3+2x^2-3x-15\right)\)
\(=\left(2x^3-3x+1\right)-\left(2x^3+2x^2-3x-15\right)\)
\(=2x^3-3x+1-2x^3-2x^2+3x+15\)
\(=\left(2x^3-2x^3\right)-2x^2+\left(-3x+3x\right)+\left(1+15\right)\)
\(=-2x^2+16\)
d) \(B\left(x\right)=Q\left(x\right)-P\left(x\right)=\left(2x^3+2x^2-3x-15\right)-\left(2x^3-3x+1\right)\)
\(=2x^3+2x^2-3x-15-2x^3+3x-1\)
\(=\left(2x^3-2x^3\right)+2x^2+\left(-3x+3x\right)+\left(-15-1\right)\)
\(=2x^2-16\)
e) Tìm nghiệm
\(A\left(x\right)=-2x^2+16.\)
\(A\left(x\right)=0\Leftrightarrow-2x^2=0-16=-16\Leftrightarrow x^2=\frac{-16}{-2}=8\)\(\Leftrightarrow\orbr{\begin{cases}x=-\sqrt{8}\\x=\sqrt{8}\end{cases}}\)
f) Tìm nghiệm
\(B\left(x\right)=2x^2-16\)
\(B\left(x\right)=0\Leftrightarrow2x^2=0+16=16\Leftrightarrow x^2=\frac{16}{2}=8\Leftrightarrow\orbr{\begin{cases}x=-\sqrt{8}\\x=\sqrt{8}\end{cases}}\)
