a²b²c²(1/a³ + 1/b³ + 1/c³) = b²c²/a + a²c²/b + a²b²/c = (b/a)bc² + a²c(c/b) + a²b(b/c) = qbc² + a²c(q) + a²b(1/q) = c³+ aqac +a³ = c³ + ba(bq) + a³ = a³ + b(aq)b + c³ = a³+b³+c³
(a+b+c)(a-b+c) = (a+c+b)(a+c-b) = (a+c)² - b² = a² + 2ac + c² - b² = a² + 2(b/q)(bq) + c² - b² = a² + 2b² + c² - b² = a² + b² + c²