64^2x + 64^2y = 12

64^x+y=4 корня из 2. система.

Ответ

корень 5 степ. из (128x^2) = 24 + корень 5 степ. из (64 х)

(128x^2) ^ (1/5) = 24 + (64x) ^ (1/5)

128^ (1/5) * x^ (2/5) = 24 + 64^ (1/5) * x^ (1/5)

(2^7) ^ (1/5) * x^ (2/5) = 24 + (2^6) ^ (1/5) * x^ (1/5)

2^ (5/5) * 2^ (2/5) * x^ (2/5) = 24 + (2^5/5) * 2^ (1/5) * x^ (1/5)

2 * (2x) ^ (2/5) - 2 * (2x) ^ (1/5) - 24 = 0

(2x) ^ (2/5) - (2x) ^ (1/5) - 12 = 0

(2x) ^ (1/5) = t

t^2 - t - 12 = 0

t1 = 4 = > (2x) ^ (1/5) = 4 = > 2x = 4^5 = 1024 = > x = 1024/2 = 512

t2 = - 3 = > (2x) ^ (1/5) = - 3 = > 2x = (-3) ^5 = - 243 = > x = - 243/2 = - 121.5