2023 A Level H3 Mathematics solutions
Solutions to 2023 A Level H3 MathematicsQuestion 11(a) Prove that, for any real numbers $a_1,a_2,\dots,a_n$,
a_1 + a_2 + \cdots + a_n \leq \sqrt{n}\sqrt{a_1^2 + a_2^2 + \cdots + a_n^2}1(b) Prove that, for any positive real numbers $x, y$ and $z$,
\sqrt{\frac{x+y}{x+y+z}} + \sqrt{\frac{y+z}{x+y+z}} + \sqrt{\frac{z+x}{x+y+z}} \leq \sqrt{6}1(c) Hence solve the equation
2\bigg(\sqrt{\frac{x+3}{x+6}}\bigg) + \sqrt{\frac{6}{x+6}} = \sqrt{6}
Proof
For part (a), it suff ...
test
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