f = 5^(x + a) - 7^x
g = 5^x - 7^(x + b)
h = (5^(x + a) - 7^x) + (5^x - 7^(x + b))
h = 5^x·(5^a + 1) - 7^x·(7^b + 1)
h = 2·(13·5^x - 25·7^(x - 2))
h = 26·5^x - 50·7^(x - 2)---> h = 26·5^x - 50/49·7^x
Deve essere:
{5^a + 1 = 26---> a = 2
{7^b + 1 = 50/49---> b = -2
Quindi:
f = 5^(x + 2) - 7^x ; g = 5^x - 7^(x - 2)
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f - 49·g ≥ - 48/25
(5^(x + 2) - 7^x) - 49·(5^x - 7^(x - 2)) + 48/25 ≥ 0
24·(2 - 5^(x + 2))/25 ≥ 0
2 - 5^(x + 2) ≥ 0---> x ≤ LN(2)/LN(5) - 2
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φ = ABS(7^x + (5^(x + 2) - 7^x) - 2)
φ = ABS(5^(x + 2) - 2)