How many real pairs of satisfy the system above?
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Use AM-GM for the second equation 7 = 5 . 5 3 x + 3 . 3 2 y ≥ 8 8 5 5 3 2 . 2 3 x 5 y 3 = 8 As can be seen, the inequality above is wrong so N o n e is the correct answer
*For anyone that questioned: " x , y aren't positive so we can't use AM-GM". In the first equation, notice that x , y have odd power, and R H S > 0 , so x , y must be both positive or both negative. If they're negatives, then the second equation'll be incorrect since L H S < 0 and R H S > 0 . Therefore they must be positive