Question 80

$$x = 5 + \sqrt[3]{5} + \sqrt[3]{25} \Rightarrow x^3 - 15x^2 + 60x + 10 =$$

Solution

$$(x - 5)^3 = 5 + 25 + 3 \times 5 (x - 5)$$

$$(x - 5)^3 = 30 + 15 (x - 5)$$

$$(x - 5)[x^2 + 25 - 10x - 15] = 30$$

$$(x - 5)[x^2 - 10x + 10] = 30$$

$$x^3 - 15x^2 + 60x - 50 = 30$$

$$x^3 - 15x^2 + 60x = 30 + 15$$

$$x^3 - 15x^2 + 60x + 10 = 90$$

Hence the answer is option C

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