Question

решить систему уравнений
4^x*4^y=64
4^x-4^y=63

Answer 1

4^x * 4^y = 64
4^x - 4^y = 63

4^x = a
4^y = b

ab = 64
a - b = 63

a = 63 + b
b(63 + b) = 64

a = 63 + b
b² + 63b - 64 = 0

a = 63 + b
b₁ = -64   <=  4^y > 0 ⇒ -64 - посторонний корень
b₂ = 1

b = 1
a = 64

4^y = 1
4^x = 64

y = 0
x = 3

Ответ: (3; 0)