Question

Cho a,b,c CMR

\(a,a^2+b^2\ge\dfrac{\left(a+b\right)^2}{2}\)

\(b,a^4+b^4\ge\dfrac{\left(a+b\right)^4}{8}\)

\(c,a^2+b^2+c^2\ge\dfrac{\left(a+b+c\right)^2}{3}\)

\(d,a^4+b^4+c^4\ge\dfrac{\left(a+b+c\right)^4}{27}\)

MÌNH CẦN GẤP GIÚP MÌNH NHA

Answer 1

Câu a : \(a^2+b^2\ge\dfrac{\left(a+b\right)^2}{2}\Leftrightarrow\left(a-b\right)^2\ge0\)

Answer 2

a: =>2a^2+2b^2>=a^2+2ab+b^2

=>a^2-2ab+b^2>=0

=>(a-b)^2>=0(luôn đúng)

c: =>3a^2+3b^2+3c^2>=a^2+b^2+c^2+2ab+2bc+2ac

=>2a^2+2b^2+2c^2-2ab-2bc-2ac>=0

=>(a-b)^2+(b-c)^2+(a-c)^2>=0(luôn đúng)