x = √5+√4 হলে x2 + 1/x2 এর মান কত?
Solution
Correct Answer: Option C
দেওয়া আছে,
x = √5 + √4
⇒ 1/x = 1/(√5 + √4)
⇒ 1/x = (√5 - √4)/{(√5 + √4)(√5 - √4)}
⇒ 1/x = (√5 - √4)/{(√5)2 - (√4)2}
⇒ 1/x = (√5 - √4)/(5 - 4)
⇒ 1/x = √5 - √4
আবার,
x + 1/x = √5 + √4 + √5 - √4
⇒ x + 1/x = 2√5
সুতরাং,
x2 + 1/x2 = (x + 1/x)2 - 2.x.(1/x)
⇒ x2 + 1/x2 = (2√5)2 - 2
⇒ x2 + 1/x2 = 4 × 5 - 2
⇒ x2 + 1/x2 = 20 - 2
⇒ x2 + 1/x2 = 18
x = √5 + √4
⇒ 1/x = 1/(√5 + √4)
⇒ 1/x = (√5 - √4)/{(√5 + √4)(√5 - √4)}
⇒ 1/x = (√5 - √4)/{(√5)2 - (√4)2}
⇒ 1/x = (√5 - √4)/(5 - 4)
⇒ 1/x = √5 - √4
আবার,
x + 1/x = √5 + √4 + √5 - √4
⇒ x + 1/x = 2√5
সুতরাং,
x2 + 1/x2 = (x + 1/x)2 - 2.x.(1/x)
⇒ x2 + 1/x2 = (2√5)2 - 2
⇒ x2 + 1/x2 = 4 × 5 - 2
⇒ x2 + 1/x2 = 20 - 2
⇒ x2 + 1/x2 = 18
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