Quantitative Aptitude Ques 1895

Question: If $ x=p+\frac{1}{p} $ and $ y=p-\frac{1}{p}, $ then value of $ x^{4}-2x^{2}y^{2}+y^{4} $ is

Options:

A) 24

B) 4

C) 16

D) 8

Show Answer

Answer:

Correct Answer: C

Solution:

  • Given, $ x=p+\frac{1}{p} $ and $ y=p-\frac{1}{p} $ $ x^{2}-2x^{2}y^{2}+y^{4}={{[(x^{2}-y^{2})]}^{2}} $ $ ={{[(x+y)(x-y)]}^{2}} $ $ ={{[ ( p+\frac{1}{p}+p-\frac{1}{p} )( p+\frac{1}{p}-p+\frac{1}{p} ) ]}^{2}} $ [putting the value of a and y] $ ={{[ (2p)( \frac{2}{p} ) ]}^{2}}=4p^{2}\times \frac{4}{p^{2}}=4\times 4=16 $
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