A²/5 + 5/a² = a⁴/(5a²) + 25/(5a²) = (a⁴ + 25)/(5a²) = (a⁴ + 25 + 10a² - 10a²)/(5a²) = (a⁴ - 10a² + 25 + 10a²)/(5a²) = ((a² - 5)² + 10a²)/(5a²) = (a² - 5)²/(5a²) + (10a²)/(5a²) = (1/5)*((a² - 5)/a)² + (10a²)/(5a²) = (1/5)*((a² - 5)/a)² + 2
a - 5/a = 10
(a² - 5)/a² = 10
(1/5)*((a² - 5)/a)² + 2 = (1/5)*(10)² + 2 = (1/5)*100 + 2 = 20+2 = 22