Chứng minh bất đẳng thức bằng phương pháp sử dụng...

A \(a + b + c \geqslant 0\)

B \(a,b,\,c \in \mathbb{R}\)

C \(a + b + c < 0\)

D \(ab + bc + ca > 0\)

A \({x^2} + 9 \geqslant 6x.\)

B \({x^2} + 9 < 6x.\)

C \({x^2} + 1 < 2x.\)

D \({x^2} + 4 < 4x.\)

A \(x \in \mathbb{R}.\)

B \(x < 2.\)

C \(x >  - 1.\) 

D \(x > \dfrac{{20}}{{23}}.\)

A \(\dfrac{8}{{11}}\)

B \(\dfrac{{11}}{8}.\)

C \(2\)

D \(\dfrac{1}{2}\)

A \(a + c > b + d\)

B \(a - c > b - d\)

C \(ac > bd\)

D \({a^2} > {b^2}\)

A \(4a + 5c < 4b + 5c\)

B \({a^2} < {b^2}\)

C \(ac > bc\)

D \(ac < bc\)

A \(\dfrac{{a + b}}{2} > a\)

B \(\dfrac{{a + b}}{2} < b\)

C \(b < \dfrac{{a + b}}{2} < a\)

D \(A,\,B,\,C\) đều sai.

A \(x \in \mathbb{R}\)

B \(x < 0\)

C \(x \geqslant 0\)

D \(x \in \mathbb{R}\backslash \left\{ { \pm 1} \right\}.\)

A \(16\) 

B \(32\)

C \(4\)

D \(2\) 

A \(ab \geqslant 1\)

B \(ab <  - 1\)

C \(ab \ne  - 1.\)

D Đáp án A và B.

A \(\dfrac{1}{2}\)

B \(1\)  

C \(2\)

D \(\dfrac{3}{2}\)

A \(ab > ad + bc\)

B \(a - c > d\) 

C \(b - d > c\)

D \(ab < ad + bc\)

A \({31^{11}} > {17^{14}}\)

B \({31^{11}} = {17^{14}}\)

C \({31^{11}} < {17^{14}}\)

D Tất cả các đáp án đều sai.

A \(2\)

B \(1\)

C \(0\)

D \( - 1\)

A \( - 1\)

B \(0\)

C \(1\) 

D \(2\)