x = √5 + √4 হলে x2 + (1/x2) এর মান কত?
সমাধান
সঠিক উত্তর: Option C
দেওয়া আছে,
x = √5 + √4
1/x = 1/(√5 + √4)
= (√5 - √4)/(√5 - √4) (√5 + √4)
= (√5 - √4)/(√5)2 - (√4)2
= (√5 - √4)/(5 - 4)
= (√5 - √4)/1
1/x = √5 - √4
এখন,
x + 1/x = √5+ √4 + √5 - √4
= 2√5
∴ x2 + (1/x2) = (x + 1/x)2 - 2 . x . 1/x
= (2√5)2 - 2
= 20 - 2
= 18
x = √5 + √4
1/x = 1/(√5 + √4)
= (√5 - √4)/(√5 - √4) (√5 + √4)
= (√5 - √4)/(√5)2 - (√4)2
= (√5 - √4)/(5 - 4)
= (√5 - √4)/1
1/x = √5 - √4
এখন,
x + 1/x = √5+ √4 + √5 - √4
= 2√5
∴ x2 + (1/x2) = (x + 1/x)2 - 2 . x . 1/x
= (2√5)2 - 2
= 20 - 2
= 18
