Question

Cho \(a\ge4;ab\ge12.\)Chứng minh rằng \(C=a+b\ge7\)

Answer 1

Ta có:\(C=a+b\)

\(C=\dfrac{9}{12}a+b+\dfrac{3}{12}a\)

\(C\ge2\sqrt{\dfrac{9}{12}ab}+\dfrac{3}{12}.4\)(AM-GM)

\(C\ge2\sqrt{\dfrac{9}{12}.12}+1\)

\(C\ge2.3+1=7\left(\text{đ}pcm\right)\)

"="<=>a=4;b=3

Answer 2

Do : a ≥ 4

⇒ b ≥ \(\dfrac{12}{a}\) ≥ 3

⇒ a + b ≥ 4 + 3

⇒ a + b ≥ 7 ( chắc thế :D)

Answer 3

Help me mn!