x = √3 + √2 হলে x3 + 1/x3 এর মান কত?
Solution
Correct Answer: Option B
দেওয়া আছে,
x = √3 + √2
⇒ 1/x = 1/(√3 + √2)
⇒ 1/x = (√3 - √2)/(√3 + √2)(√3 - √2)
⇒ 1/x = (√3 - √2)/ (3-2)
⇒ 1/x = (√3 - √2)
x + 1/ x = √3 + √2 + √3 - √2
= 2√3
x3 + 1/x3 = (x + 1/x)3 - 3.x.(1/x)(x + 1/x)
= (2√3)3 - 3 × 2√3
= 24√3 - 6√3
= 18√3
x = √3 + √2
⇒ 1/x = 1/(√3 + √2)
⇒ 1/x = (√3 - √2)/(√3 + √2)(√3 - √2)
⇒ 1/x = (√3 - √2)/ (3-2)
⇒ 1/x = (√3 - √2)
x + 1/ x = √3 + √2 + √3 - √2
= 2√3
x3 + 1/x3 = (x + 1/x)3 - 3.x.(1/x)(x + 1/x)
= (2√3)3 - 3 × 2√3
= 24√3 - 6√3
= 18√3
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