a = √3 + √2 হলে a³+1/a³ এর মান নির্ণয় করুন।

A 6√2

B 18√3

C 9√2

D 8√3

Solution

Correct Answer: Option B

Given, a = √3 + √2
or, 1/a = 1/(√3 + √2) = (√3 - √2)/((√3 + √2)(√3 - √2)) = √3 - √2

∴ a + 1/a = √3 + √2 + √3 - √2 = 2√3
Or, a + 1/a = 2√3
Or, ( a + 1/a) = 2√3
Or, ( a + 1/a)³ = (2√3)³
Or, a³ + 1/a³ + 3.a.1/a ( a+1/a) = 24√3
Or, a³ + 1/a³ + 3.2√3 = 24√3
Or, a³ + 1/a³ + 6√3 = 24√3
Or, a³ + 1/a³ = 24√3 - 6√3
Or, a³ + 1/a³ = 18√3

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