Question

CMR: thương phép chia sau lớn hơn 0 với mọi x

[(x^4+1)^5-2(x^4+1)^4+3(x^4+1)^3]:(x^4+1)^3

CMR: phép chia sau luôn âm

[-(x^2+y^2)^4-4(x^2+y^2)^3-5(x^2+y^2)^2]:(x^2+y^2)^2

^2 ý là: mũ 2

Answer 1

a/

\(=\left(x^4+1\right)^2+2\left(x^4+1\right)+3\)

\(=\left(x^4+2\right)^2+2>0\forall x\) (do \(\left(x^4+2\right)^2>0\forall x\)

b/

\(=-\left(x^2+y^2\right)^2-4\left(x^2+y^2\right)-5\)

\(=-\left(x^2+y^2+4\right)^2-1< 0\forall x\) (do...)