Question

Find the value of the cubic polynomial x3 – 5x2 + 8x-4 if: x= 1/8-root of 60

Answer 1

Answer:

Step-by-step explanation:

-354.4 is the answer

Answer 2

$Given \: x = \frac{1}{(8-\sqrt{60})}$

$\implies x = \frac{(8+\sqrt{60})}{ 8^{2} - (\sqrt{60})^{2}} \\= \frac{(8+2\sqrt{15})}{ 64 - 60} \\= \frac{2(4+\sqrt{15})}{ 4} \\=\frac{(4+\sqrt{15})}{ 2} \: --(1)$

$\red{ Value \:of \: x^{3} - 5x^{2} + 8x - 4 } \\= \Big(\frac{(4+\sqrt{15})}{ 2}\Big)^{3} \\-5\Big(\frac{(4+\sqrt{15})}{ 2}\Big)^{2}\\ + 8\Big( \frac{(4+\sqrt{15})}{ 2}\Big)\\ - 4$

$= \frac{64+15\sqrt{15}+48\sqrt{15}+180}{8} \\-\frac{5(16+15+8\sqrt{15})}{4} \\+\frac{8(4+\sqrt{15})}{2}\\-4$

$= \frac{64+63\sqrt{15}+180-10(31+8\sqrt{15})-32(4+\sqrt{15})-32}{8}$

$\green { =\frac{-226-49\sqrt{15}}{8}}$

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