Cho `a+b= \sqrt{9+4\sqrt{5}}-\sqrt{5}`. Tính P`=a^3-b^3+6ab+2016`
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Đáp án:
$\begin{array}{l}
a + b = \sqrt {9 + 4\sqrt 5 } - \sqrt 5 \\
= \sqrt {{{\left( {\sqrt 5 + 2} \right)}^2}} - \sqrt 5 \\
= \sqrt 5 + 2 - \sqrt 5 \\
= 2\\
\Leftrightarrow a = 2 - b\\
P = {a^3} - {b^3} + 6ab + 2016\\
= {\left( {2 - b} \right)^3} - {b^3} + 6\left( {2 - b} \right).b + 2016\\
= 8 - 12b + 6{b^2} - {b^3} - {b^3} + 12b - 6{b^2} + 2016\\
= 2014 - 2{b^3}
\end{array}$