Question

Cho 3 số a, b, c thỏa a + b + c = \(\dfrac{3}{2}\)

Chứng minh:

\(a^2 + b^2 + c^2 ≥ \dfrac{3}{4}\)

Answer 1

\(a^2+\dfrac{1}{4}>=2\cdot a\cdot\dfrac{1}{2}=a\)

\(b^2+\dfrac{1}{4}>=b\)

c^2+1/4>=c

=>a^2+1/4+b^2+1/4+c^2+1/4>=a+b+c

=>a^2+b^2+c^2>=3/4