Question

The sum of the square of a rational number and the square of its reciprocal is 7/4 more
than the sum of that rational number and its recíprocal. Find
the number???​

Answer 1

Answer:

p^2 + 1/p^2= (p+1/p) + 7/4

p^2 + 1/p^2 + 2.p.(1/p)=(p+1/p) +7/4 + 2p.(1/p)

(p+1/p)^2 = (p+1/p) +7/4+2

let p+1/p = a

a^2 =a + 15/4

4a^2 -4a -15=0

(2a-5)(2a+3)=0

2a=5

a =5/2

p+1/p=5/2

2p^2-5p+2=0

2p^2-4p-p+2=0

2p(p-2)-(p-2)=0

(2p-1)(p-2)=0

p=1/2 p=2

you can do the other factor 2a+3 in the same way