Wykaż, że jeśli a≠0 i b≠0 oraz a/b+ b/a=2, to a=b
a b
--- + ...... = 2
b a
a² + b²
---------- = 2
ab
2ab = a² + b²
a² - 2ab + b² = 0
(a - b)² = 0²
a - b = 0
a = b
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a b
--- + ...... = 2
b a
a² + b²
---------- = 2
ab
2ab = a² + b²
a² - 2ab + b² = 0
(a - b)² = 0²
a - b = 0
a = b