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p and q are positive integers and \(\frac{p}{q} + \frac{q}{p} = 3,\) then, \(\frac{p^2}{q^2} + \frac{q^2}{p^2} = \)

A.
3
B.
7
C.
9
D.
11

Solution:

Concept:Integers: Integers are the positive numbers that can be negative, positive, and zero but cannot be fractions Examples: .......-2,-1,0,1,2.......Calculation:Given:\(\frac{p}{q}\ +\ \frac{q}{p}\ =\ 3\).........(1)Where p and q are positive integersNow by squaring on both sides of equation (1) we get\(\left ( \frac{p}{q}\ +\ \frac{q}{p} \right )^2\ =\ 3^2\)\(\frac{p^2}{q^2}\ +\ \frac{q^2}{p^2}\ +\ 2\ \times\ \frac{p}{q}\ \times\ \frac{q}{p}\ =\ 9\)\(\frac{p^2}{q^2}\ +\ \frac{q^2}{p^2}\ +\ 2\ \ =\ 9\)? \(\frac{p^2}{q^2}\ +\ \frac{q^2}{p^2}\ =\ 7\)Download Solution PDFShare on Whatsapp

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