Question

Решите систему уравнений $left { {{2^x+2^y=10} atop {x+y=4}} right.$

Answer 1

2^x + 2^y = 10
x+y=4
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x=4-y
2^(4-y) + 2^y = 10
2^4/2^y + 2^y = 10
16/2^y + 2^y = 10
16 + (2^y)^2 - 10*2^y = 0
2^y=t t>0
t^2 - 10y + 16 =0
D=100-4*16=36=6^2
t12= (10+-6)/2 = 8 2
2^y=2
y=1
x+y=4
x=3
2^y=8
2^y=2^3
y=3
x+y=4
x=1
ответ (1 3) (3 1)