Question

If a+1/a =p and a-1/a=q,find the relation between p and q.

Answer 1

a+1/a = p

squaring both sides,

(a+1/a)² = p²
⇒(a²+1/a² +2) = p²

subtracting both sides 4,

(a²+1/a²+2) -4 = p²-4
⇒(a²+1/a²-2) = p² -4
⇒(a-1/a)² = p² -4
⇒q² = p² - 4
⇒p² - q² = 4

This is the required relation.

Answer 2

Answer:

It is given that,

a+1/a=p and a−1/a=q

so,

(a+1/a)

2

−(a−1/a)

2

=4(a)(1/a)

=4

By substituting the values, we get

p

2

−q

2

=4

Hence the relation between p and q is that p

2

−q

2

=4.