SATHEE: Quantitative Aptitude Ques 1374

Quantitative Aptitude Ques 1374

Question: $ x=3+2\sqrt{2}, $ then the values of $ x^{3}+\frac{1}{x^{3}} $ and $ x^{3}-\frac{1}{x^{3}} $ are respectively

Options:

A) $ 140\sqrt{2}, $ $ 198 $

B) $ 234, $ $ 216 $

C) $ 216, $ $ 234 $

D) $ 198, $ $ 140\sqrt{2} $

Show Answer

Answer:

Correct Answer: D

Solution:

Given, $ x=3+2\sqrt{2} $ $ \frac{1}{x}=\frac{1}{3+2\sqrt{2}}\times \frac{3-2\sqrt{2}}{3-2\sqrt{2}} $ $ =3-2\sqrt{2} $ [on rationalising]

$ \therefore $ $ x^{3}+\frac{1}{x^{3}}={{(3+2\sqrt{2})}^{3}}+{{(3-2\sqrt{2})}^{3}} $ $ =27+16\sqrt{2}+3\times 9\times 2\sqrt{2}+3\times 3\times 8+27-16\sqrt{2} $ $ -3\times 9\times 2\sqrt{2}+3\times 3\times 8 $ $ =27+72+27+72=198 $ Now, $ x^{3}-\frac{1}{x^{3}}={{(3+2\sqrt{2})}^{3}}-{{(3-2\sqrt{2})}^{3}} $ $ =27+16\sqrt{2}+3\times 9\times 2\sqrt{2}+3\times 3\times 8-27 $ $ +16\sqrt{2}+3\times 9\times 2\sqrt{2}-3\times 3\times 8 $ $ =16\sqrt{2}+54\sqrt{2}+16\sqrt{2}+54\sqrt{2}=140\sqrt{2} $

Quantitative Aptitude Ques 1373

Quantitative Aptitude Ques 1375

Quantitative Aptitude Ques 1374

Question: $ x=3+2\sqrt{2}, $ then the values of $ x^{3}+\frac{1}{x^{3}} $ and $ x^{3}-\frac{1}{x^{3}} $ are respectively

Options:

Answer:

Solution:

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