Câu hỏi của yasuo Nguyen

Question

c/m bat dang thuc sau:4a^4-4a^3=>4a-1-5a^2 voi moi a

Đinh quang hiệp · Accepted Answer

$\Rightarrow4a^4-4a^3-4a+1+5a^2>=0$

$\Rightarrow\left(4a^4-4a^3+a^2\right)+\left(4a^2-4a+1\right)>=0$

$\Rightarrow\left(\left(2a^2\right)^2-2\cdot2a^2a+a^2\right)+\left(\left(2a\right)^2-2\cdot2a+1^2\right)>=0$

$\Rightarrow\left(2a^2-a\right)^2+\left(2a-1\right)^2>=0$

vì $\left(2a^2-a\right)^2>=0$với mọi a $\left(2a-1\right)^2>=0$với mọi a

$\Rightarrow\left(2a^2-a\right)^2+\left(2a-1\right)^2>=0$với mọi a

$\Rightarrow$đpcm

Câu trả lời:

$\Rightarrow4a^4-4a^3-4a+1+5a^2>=0$

$\Rightarrow\left(4a^4-4a^3+a^2\right)+\left(4a^2-4a+1\right)>=0$

$\Rightarrow\left(\left(2a^2\right)^2-2\cdot2a^2a+a^2\right)+\left(\left(2a\right)^2-2\cdot2a+1^2\right)>=0$

$\Rightarrow\left(2a^2-a\right)^2+\left(2a-1\right)^2>=0$

vì $\left(2a^2-a\right)^2>=0$với mọi a $\left(2a-1\right)^2>=0$với mọi a

$\Rightarrow\left(2a^2-a\right)^2+\left(2a-1\right)^2>=0$với mọi a

$\Rightarrow$đpcm