SOLUTION: {{{(q-p)^2 > 0}}} prove that {{{(q^3 - p^3) / (pq^2 - qp^2) > 3 }}}

Algebra ->  Inequalities -> SOLUTION: {{{(q-p)^2 > 0}}} prove that {{{(q^3 - p^3) / (pq^2 - qp^2) > 3 }}}      Log On


   

Question 979706: %28q-p%29%5E2+%3E+0 prove that %28q%5E3+-+p%5E3%29+%2F+%28pq%5E2+-+qp%5E2%29+%3E+3+
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!

%28q%5E3-p%5E3%29%2F%28pq%5E2+-+qp%5E2%29 = %28%28q-p%29%2A%28q%5E2+%2B+qp+%2B+p%5E2%29%29%2F%28pq%2A%28q-p%29%29 = %28q%5E2+%2B+qp+%2B+p%5E2%29%2F%28pq%29 = %28%28q%5E2+-+2qp+%2B+p%5E2%29+%2B+2qp+%2B+qp%29%2F%28qp%29 = %28%28q-p%29%5E2+%2B+3qp%29%2F%28qp%29 = %28q-p%29%5E2%2Fqp + %283qp%29%2Fqp%29 >= %283qp%29%2Fqp%29 = 3.

The proof is completed.