Question

If x is equal to 1 upon 3 minus root 8 find the value of x cube minus 2 x square - 7 x + 5

Answer 1

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Answer 2

Answer:

$49+16\sqrt{8}$

Step-by-step explanation:

Given,

$x=\frac{1}{3-\sqrt{8}}$

By rationalizing the denominator,

$x=\frac{1}{3-\sqrt{8}}\times \frac{3+\sqrt{8}}{3+\sqrt{8}}=\frac{3+\sqrt{8}}{3^2-(\sqrt{8})^2}=3+\sqrt{8}$

∵ a² - b² = ( a + b ) ( a - b )

$x^3=(3+\sqrt{8})^3=27+8\sqrt{8}+27\sqrt{8}+72=99+35\sqrt{8}$

∵ ( a + b )³ = a³ + 3a²b + 3ab² + b3

$x^2=9+8+6\sqrt{8}=17+6\sqrt{8}$

∵ ( a + b )² = a² + 2ab + b²

$2x^2 = 34+12\sqrt{8}$

$7x=21+7\sqrt{8}$

$\implies x^3 - 2x^2 - 7x + 5 = 99+35\sqrt{8} - 34-12\sqrt{8}- 21-7\sqrt{8}+5$

$=49+16\sqrt{8}$