यदि \(\alpha=1+\sqrt{2}\) और \(\beta=1-\sqrt{2}\), तो \(\alpha^3+\beta^3\) क्या है?
If \(\alpha=1+\sqrt{2}\) and \(\beta=1-\sqrt{2}\), what is \(\alpha^3+\beta^3\)?
Explanation opens after your attempt
Correct Answer
A. (14)
Concept
\(\alpha+\beta=2\) and \(\alpha\beta=-1\), so (\alpha-3+\beta-3=23-3(-1)(2)=14). Use (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)).
Why this answer is correct
The correct answer is A. (14). \(\alpha+\beta=2\) and \(\alpha\beta=-1\), so (\alpha-3+\beta-3=23-3(-1)(2)=14). Use (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)).
Exam Tip
\(\alpha+\beta=2\) और \(\alpha\beta=-1\), इसलिए (\alpha-3+\beta-3=23-3(-1)(2)=14)। घन योग में (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)) लगाएँ।
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