Question

Giúp mình

Answer 1

tham khảo.-.

Answer 2

Với mọi a;b dương ta có:

\(\left(x-y\right)^2\ge0\Leftrightarrow x^2+y^2\ge2xy\Leftrightarrow2x^2+2y^2\ge x^2+2xy+y^2\)

\(\Leftrightarrow2x^2+2y^2\ge\left(x+y\right)^2\)

\(\Leftrightarrow x^2+y^2\ge\dfrac{1}{2}\left(x+y\right)^2\)

Áp dụng:

\(a^4+b^4\ge\dfrac{1}{2}\left(a^2+b^2\right)^2\ge\dfrac{1}{2}\left[\dfrac{1}{2}\left(a+b\right)^2\right]^2>\dfrac{1}{2}\left[\dfrac{1}{2}.1^2\right]^2=\dfrac{1}{8}\) (đpcm)