gaokao 2022 Q23

gaokao · China · national-A-science 10 marks Proof Direct Proof of an Inequality

[Elective 4-5: Inequalities] (10 points) Given that $a$, $b$, $c$ are all positive numbers and $a ^ { 2 } + b ^ { 2 } + 4 c ^ { 2 } = 3$, prove that:
(1) $a + b + 2 c \leq 3$;
(2) If $b = 2 c$, then $\frac { 1 } { a } + \frac { 1 } { c } \geq 3$.

[Elective 4-5: Inequalities] (10 points)\\
Given that $a$, $b$, $c$ are all positive numbers and $a ^ { 2 } + b ^ { 2 } + 4 c ^ { 2 } = 3$, prove that:\\
(1) $a + b + 2 c \leq 3$;\\
(2) If $b = 2 c$, then $\frac { 1 } { a } + \frac { 1 } { c } \geq 3$.

Paper Questions

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