надо подметить, что
16 = 4 * 4
28 = 4 * 7
49 = 7 * 7
16/28 = 4/7
49/28 = 7/4
7*49^x + 3*28^x = 4* 16^x
делим на 28^x - не ноль
7*7^2x/(4^x*7^x) + 3 = 4* 4^2x/(4^x*7^x)
7*(7/4)^x - 4*(4/7)^x + 3 = 0
(7/4)^x = t > 0
7t - 4/t + 3 = 0
7t² + 3t - 4 = 0
D = 9 + 4*4*7 = 121 = 11²
t12 = (-3 +- 11)/14 = - 1 8/14(=4/7)
t1 = -1 нет t>0
t2 = 4/7
(7/4)^x = 4/7
(7/4)^x = (7/4)^-1
x = -1
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Verified answer
надо подметить, что
16 = 4 * 4
28 = 4 * 7
49 = 7 * 7
16/28 = 4/7
49/28 = 7/4
7*49^x + 3*28^x = 4* 16^x
делим на 28^x - не ноль
7*7^2x/(4^x*7^x) + 3 = 4* 4^2x/(4^x*7^x)
7*(7/4)^x - 4*(4/7)^x + 3 = 0
(7/4)^x = t > 0
7t - 4/t + 3 = 0
7t² + 3t - 4 = 0
D = 9 + 4*4*7 = 121 = 11²
t12 = (-3 +- 11)/14 = - 1 8/14(=4/7)
t1 = -1 нет t>0
t2 = 4/7
(7/4)^x = 4/7
(7/4)^x = (7/4)^-1
x = -1