Question

1/p+1/q = 1/p+q
Then p3 - q3 =?

Answer 1

Answer:

Step-by-step explanation:

Since, (p+q) = 3

Cubing on both the sides of the equation, we get

(p+q)^3 = (3)^3

By using the algebraic identity (a+b)^3 = a^3 + b^3 +3ab(a+b)

Consider (p+q)^3 = (3)^3

p^3 + q^3 +3pq(p+q)=(3)^3

Now, as p = \frac{1}{q}

p^3 + q^3 +3(\frac{1}{q})q(p+q)=27

Also, p+q = 3, we get

p^3 + q^3 +3(3)=27

p^3 + q^3=27-9 = 18

Therefore, the value of p^3 + q^3 is 18.