Here \(\alpha+\beta=3\) and \(\alpha\beta=\frac{5}{4}\). Thus \(\alpha^3+\beta^3=27-\frac{45}{4}=\frac{63}{4}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{63}{4}\). Here \(\alpha+\beta=3\) and \(\alpha\beta=\frac{5}{4}\). Thus \(\alpha^3+\beta^3=27-\frac{45}{4}=\frac{63}{4}\).
Step 3
Exam Tip
यहाँ \(\alpha+\beta=3\) और \(\alpha\beta=\frac{5}{4}\) है। \(\alpha^3+\beta^3=27-\frac{45}{4}=\frac{63}{4}\)।
Here \(\alpha+\beta=3\) and \(\alpha\beta=\frac{5}{4}\). Using (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)), we get \(\frac{63}{4}\), so none of the options is correct.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{81}{8}\). Here \(\alpha+\beta=3\) and \(\alpha\beta=\frac{5}{4}\). Using (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)), we get \(\frac{63}{4}\), so none of the options is correct.
Step 3
Exam Tip
यहाँ \(\alpha+\beta=3\) और \(\alpha\beta=\frac{5}{4}\) है। (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=\frac{63}{4}), इसलिए विकल्पों में कोई सही नहीं है।
Here \(\alpha+\beta=\frac{8}{3}\) and \(\alpha\beta=\frac{4}{3}\). Using (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)), we get \(\frac{224}{27}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{224}{27}\). Here \(\alpha+\beta=\frac{8}{3}\) and \(\alpha\beta=\frac{4}{3}\). Using (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)), we get \(\frac{224}{27}\).
Step 3
Exam Tip
यहाँ \(\alpha+\beta=\frac{8}{3}\) और \(\alpha\beta=\frac{4}{3}\) है। (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)) से \(\frac{224}{27}\) मिलता है।
Here \(\alpha+\beta=\frac{5}{2}\) and \(\alpha\beta=\frac{3}{2}\). Using (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)), we get \(\frac{35}{8}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{35}{8}\). Here \(\alpha+\beta=\frac{5}{2}\) and \(\alpha\beta=\frac{3}{2}\). Using (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)), we get \(\frac{35}{8}\).
Step 3
Exam Tip
यहाँ \(\alpha+\beta=\frac{5}{2}\) और \(\alpha\beta=\frac{3}{2}\) है। (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)) से \(\frac{35}{8}\) मिलता है।
