x = √2 + √3 হলে, x3 + 1/x3 এর মান কত?
Solution
Correct Answer: Option B
দেওয়া আছে,
x = √2 + √3
1/x = 1/(√2 + √3)
1/x = (√3 - √2)/(√3 - √2)(√2 + √3)
1/x = (√3 - √2)/{(√3)2 - (√2)2}
1/x = (√3 - √2)/(3 - 2)
1/x = (√3 - √2)/1
1/x = √3 - √2
x + 1/x = √2 + √3 + √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 = √2 + √3
1/x = 1/(√2 + √3)
1/x = (√3 - √2)/(√3 - √2)(√2 + √3)
1/x = (√3 - √2)/{(√3)2 - (√2)2}
1/x = (√3 - √2)/(3 - 2)
1/x = (√3 - √2)/1
1/x = √3 - √2
x + 1/x = √2 + √3 + √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
Practice More Questions on Our App!
Download our app for free and access thousands of MCQ questions with detailed solutions