If x = 711-62, find the value of x3 - 9x2 + 25x - 20.
Explanation:
x = 711-62 = 73-2 = 73-2 × 3+23+2 = 3 + √2
⇒ x - 3 = √2 ...(1)
⇒ (x - 3)3 = (√2)3
⇒ x3 - 27 - 9x2 + 27x = 2√2
⇒ x3 - 27 - 9x2 + 27x = 2(x - 3) [from (1)]
⇒ x3 - 21 - 9x2 + 25x = 0
⇒ x3 - 9x2 + 25x - 20 = 1
Hence, option (b).
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