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[huyne123]

cho P=$\frac{a^3-3a+2}{a^3-4a^2+5a-2}$

biết    $a=\sqrt[3]{55+\sqrt{3024}}+\sqrt[3]{55-\sqrt{3024}}$

[Frosty Flame]

cho P=$\frac{a^3-3a+2}{a^3-4a^2+5a-2}$

biết    $a=\sqrt[3]{55+\sqrt{3024}}+\sqrt[3]{55-\sqrt{3024}}$

ĐKXĐ:$a^3-4a^2+5a-2\neq 0$

Ta có :

$a=\sqrt[3]{55+\sqrt{3024}}+\sqrt[3]{55-\sqrt{3024}}$

$<=>a^3=55+\sqrt{3024}+55-\sqrt{3024}+3(\sqrt[3]{55+\sqrt{3024}}+\sqrt[3]{55-\sqrt{3024}})\sqrt[3]{(55+\sqrt{3024})(55-\sqrt{3024})}$

$<=>a^3=110+3a<=>(a-5)(a^2+5a+22)=0<=>a=5$(T/m ĐKXĐ)

Thay $a=5$ vào

$=>P=\frac{7}{3}$

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