a = √3 - √2 হলে, a3 + 3a + 3a- 1 + a- 3 এর মান কত?
Solution
Correct Answer: Option D
দেওয়া আছে,
a = √3 - √2
⇒ 1/a = 1/(√3 - √2)
⇒ 1/a = (√3 + √2)/[(√3 - √2)(√3 + √2)]
⇒ 1/a = (√3 + √2)/{(√3)2 - (√2)2}
⇒ 1/a = √3 + √2
এখন,
a3 + 3a + 3a-1 + a-3
= a3 + 3a + 3/a + 1/a3
= (a)3 + 3a2(1/a) + 3.a.(1/a2) + (1/a)3
= (a + 1/a)3
= (√3 - √2 + √3 + √2)3
= (2√3)3
= 8 × 3√3
= 24√3
a = √3 - √2
⇒ 1/a = 1/(√3 - √2)
⇒ 1/a = (√3 + √2)/[(√3 - √2)(√3 + √2)]
⇒ 1/a = (√3 + √2)/{(√3)2 - (√2)2}
⇒ 1/a = √3 + √2
এখন,
a3 + 3a + 3a-1 + a-3
= a3 + 3a + 3/a + 1/a3
= (a)3 + 3a2(1/a) + 3.a.(1/a2) + (1/a)3
= (a + 1/a)3
= (√3 - √2 + √3 + √2)3
= (2√3)3
= 8 × 3√3
= 24√3
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