Câu 5:
Cách 1:
[TEX]a^4 + b^4 \geq \frac12(a^2+b^2)^2 + \frac18 (a+b)^4 [/TEX]
[TEX]\Rightarrow (1 + \frac{x}{y} )^4 + (1+\frac{y}{x})^4 \geq \frac18 (2 + \frac{x}{y} + \frac{y}{x} )^ 4 \geq \frac{1}{8} . 4^4 \geq 32[/TEX]
Cách 2:
[TEX](1 + \frac{x}{y} )^4 + 2^ 4+ 2^ 4+ 2^ 4 \geq 32 ( 1+ \frac{x}{y} ) [/TEX]
[TEX](1 + \frac{y}{x} )^4 + 2^ 4+ 2^ 4+ 2^ 4 \geq 32 ( 1+ \frac{y}{x} )[/TEX]
[TEX]\Rightarrow (1 + \frac{x}{y} )^4 + (1 + \frac{y}{x} )^4 + 6. 2^4 \geq 32 ( 2+ \frac{x}{y} + \frac{y}{x} ) \geq 32.4 = 2^7 [/TEX]
[TEX]\Leftrightarrow (1 + \frac{x}{y} )^4 + (1 + \frac{y}{x} )^4 \geq 2^4 (2^3 - 6) = 32[/TEX]
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
