vì a,b,c,d,e là năm nghiệm của P(x)

\(\Rightarrow P\left(x\right)=\left(x-a\right)\left(x-b\right)\left(x-c\right)\left(x-d\right)\left(x-e\right)\)

Ta có : 

\(Q\left(a\right)=a^2-2=-\left(2-a^2\right)=-\left(\sqrt{2}-a\right)\left(\sqrt{2}+a\right)=\left(\sqrt{2}-a\right)\left(-\sqrt{2}-a\right)\)

\(Q\left(b\right)=\left(\sqrt{2}-b\right)\left(-\sqrt{2}-b\right)\)

....

\(Q\left(e\right)=\left(\sqrt{2}-e\right)\left(-\sqrt{2}-e\right)\)

\(\Rightarrow Q\left(a\right).Q\left(b\right).Q\left(c\right).Q\left(d\right).Q\left(e\right)=\left(\sqrt{2}-a\right)\left(\sqrt{2}-b\right)\left(\sqrt{2}-c\right)\left(\sqrt{2}-d\right).\left(\sqrt{2}-e\right)\left(-\sqrt{2}-a\right)\left(-\sqrt{2}-b\right)\left(-\sqrt{2}-c\right)\left(-\sqrt{2}-d\right)\left(-\sqrt{2}-e\right)\)

\(=P\left(\sqrt{2}\right).P\left(-\sqrt{2}\right)=-23\)

Chắc là \(q\left(x\right)=x^2-4????\)

\(f\left(2\right)=2^5+2^2+1=37\) ; \(f\left(-2\right)=-27\)

Do \(f\left(x\right)\) có 5 nghiệm nên f(x) có dạng:

\(f\left(x\right)=\left(x-x_1\right)\left(x-x_2\right)\left(x-x_3\right)\left(x-x_4\right)\left(x-x_5\right)\)

\(\Rightarrow f\left(2\right)=\left(2-x_1\right)\left(2-x_2\right)\left(2-x_3\right)\left(2-x_4\right)\left(2-x_5\right)=37\)

\(f\left(-2\right)=\left(-2-x_1\right)\left(-2-x_2\right)\left(-2-x_3\right)\left(-2-x_4\right)\left(-2-x_5\right)=-27\)

\(\Rightarrow\left(2+x_1\right)\left(2+x_2\right)\left(2+x_3\right)\left(2+x_4\right)\left(2+x_5\right)=27\)

\(A=\left(x_1^2-4\right)\left(x^2_2-4\right)\left(x_3^2-4\right)\left(x_4^2-4\right)\left(x^2_5-4\right)\)

\(A=-\left(2-x_1\right)\left(2-x_2\right)\left(2-x_3\right)\left(2-x_4\right)\left(2-x_5\right)\left(2+x_1\right)\left(2+x_2\right)\left(2+x_3\right)\left(2+x_4\right)\left(2+x_5\right)\)

\(A=-37.27=-999\)

a: P(x)=0

=>4x-1/2=0

=>x=1/8

b: Q(x)=0

=>(x-1)(x+1)=0

=>x=1 hoặc x=-1

c: A(x)=0

=>-12x+18=0

=>-12x=-18

hay x=3/2

d: B(x)=0

=>-x²=-16

=>x=4 hoặc x=-4

e: C(x)=0

=>3x²=-12

=>\(x\in\varnothing\)

a) \(\left(1+x\right)^2+\left(1-x\right)^2\) 

\(=1+2x+x^2+1-2x+x^2\)

\(=2x^2+2\)

b) \(\left(x+2\right)^2+\left(1+x\right)\left(1-x\right)\)

\(=x^2+4x+4+1-x^2\)

\(=4x+5\)

c) \(\left(x-3\right)^2+3\left(x+1\right)^2\)

\(=x^2-6x+9+3x^2+6x+3\)

\(=4x^2+12\)

d)\(\left(2+3x\right)\left(3x-2\right)-\left(3x+1\right)^2\)

\(=9x^2-4-9x^2-6x-1\)

\(=-6x-5\)

e) \(\left(x+5\right)\left(x-2\right)-\left(x+2\right)^2\)

\(=x^2-2x+5x-10-x^2-4x-4\)

\(=-x-14\)

f) \(\left(x+3\right)\left(2x-5\right)-2\left(1+x\right)^2\)

\(=2x^2-5x+6x-15-2-4x-2x^2\)

\(=-3x-17\)

g) \(\left(4x-1\right)\left(4x+1\right)-4\left(1-2x\right)^2\)

\(=16x^2-1-4+16x-16x^2\)

\(=16x-5\)

#Học tốt!

a)\(a\left(b^3-c^3\right)+b\left(c^3-a^3\right)+c\left(a^3-b^3\right)\)

\(=a\left(b^3-c^3\right)-b\text{[}\left(b^3-c^3\right)+\left(a^3-b^3\right)\text{]}+c\left(a^3-b^3\right)\)

\(=a\left(b^3-c^3\right)-b\left(b^3-c^3\right)-b\left(a^3-b^3\right)+c\left(a^3-b^3\right)\)

\(=\left(a-b\right)\left(b^3-c^3\right)-\left(b-c\right)\left(a^3-b^3\right)\)

\(=\left(a-b\right)\left(b-c\right)\left(b^2+bc+c^2\right)-\left(b-c\right)\left(a-b\right)\left(a^2+ab+b^2\right)\)

\(=\left(a-b\right)\left(b-c\right)\left(bc+c^2-a^2-ab\right)\)

\(=\left(a-b\right)\left(b-c\right)\left(c-a\right)\left(a+b+c\right)\)