যদি x = √5 + √3 হয়, তবে x3 + 8/x3 এর মান কত?
Solution
Correct Answer: Option C
দেওয়া আছে,
x = √5 + √3
এখন,
1/x = 1/(√5 + √3)
= (√5 - √3)/{(√5 + √3)(√5 - √3)}
= (√5 - √3)/{(√5)2 - (√3)2}
= (√5 - √3)/(5 - 3)
= (√5 - √3)/2
∴ 2/x = √5 - √3
অতএব, x+ 2/x=√5 + √3 + √5 - √3=2√5
প্রদত্ত রাশি,
x3 + 8/x3 = x3 + (2/x)3
= (x + 2/x)3 - 3.x. (2/x)(x + 2/x)
= (2√5)3 - 6 × 2√5
= 40√5 - 12√5
= 28√5
Practice More Questions on Our App!
Download our app for free and access thousands of MCQ questions with detailed solutions