a) Ta có:
\(P\left(x\right)=15-4x^3+3x^2+2x-x^3-10\\ P\left(x\right)=-5x^3+3x^2+2x+5\)
\(Q\left(x\right)=5+4x^3+6x^2-5x-9x^3+7x\\ Q\left(x\right)=-5x^3+6x^2+2x+5\)
b) Ta có \(P\left(x\right)+Q\left(x\right)=-5x^3+3x^2+2x+5-5x^3+6x^2+2x+5\)
\(\Rightarrow P\left(x\right)+Q\left(x\right)=-10x^3+9x^2+4x+10\)
Thay \(x=\dfrac{1}{2}\) ta có:
\(P\left(x\right)+Q\left(x\right)=-10.\left(\dfrac{1}{2}\right)^3+9.\left(\dfrac{1}{2}\right)^2+4.\dfrac{1}{2}+10=-10.\dfrac{1}{8}+9.\dfrac{1}{4}+2+10=13\)
c) Ta có: \(Q\left(x\right)-P\left(x\right)=\left(-5x^3+6x^2+2x+5\right)-\left(-5x^3+3x^2+2x+5\right)=3x^2\)
Để \(Q\left(x\right)-P\left(x\right)=6\Rightarrow3x^2=6\)
\(\Rightarrow x^2=2\Rightarrow x=\pm\sqrt{2}\)
