Question 21

If X = $$\ \sqrt[3]{5}\ $$+ 2, then the value of $$\ x^{3}-6x^{2}\ $$+ 12x - 13 is

Solution

Given x=\sqrt[3]{5}+2

$$\ x^{3}-6x^{2}\ $$+ 12x - 13

= $$(\sqrt[3]{5}+2)^{3}-6(\sqrt[3]{5}+2)^{2}+12(\sqrt[3]{5}+2)-13$$

= $$(5+8+6\times5^{\frac{2}{3}}+12\times5^{\frac{1}{3}})-6[5^{\frac{1}{3}}+4+4\times5^{\frac{1}{3}}]+12(5^{\frac{1}{3}}+2)-13$$

= $$13+6\times5^{\frac{2}{3}}+12\times5^{\frac{1}{3}}-6\times5^{\frac{2}{3}}-24-24\times5^{\frac{1}{3}}+12\times5^{\frac{1}{3}}+24-13$$

= 0

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