Toán Lớp 9: Cho a+b= \sqrt{9+4\sqrt{5}}-\sqrt{5}. Tính P=a^3-b^3+6ab+2016
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Toán Lớp 9: Cho a+b= \sqrt{9+4\sqrt{5}}-\sqrt{5}. Tính P=a^3-b^3+6ab+2016
Comments ( 1 )
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}$