Крик души. решите подробно. система уравнении. {8^x+8^y=72 {x+y=3 найдите |x1-x2| ответ будет: 1

{x+y=3
{8^x+8^y=72

{x=3-y
{8^(3-y)+8^y=72

8^(3-y) + 8^y = 72
8^3/8^y + 8^y = 72
(8^3 + (8^y)*(8^y) - 72*8^y)/8^y = 0
(8^y)^2 - 72*8^y + 8^3 = 0
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8^y=t

t^2 - 72t + 8^3 = 0
D= (9^2)*(8^2) - 4*8^3 = (8^2)*(81-32) = (8^2)*(7^2) = 56^2

[t1=(72+56)/2=64
[t2=(72-56)/2=8

[ {t1=64
[ {8^y1=8^2 <=> y1=2
[
[ {t1=8
[ {8^y2=8 <=> y2=1
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[ {y1=2
[ {x1=3-2=1
[
[ {y2=1
[ {x2=3-1=2

|x1-x2| = |1-2| = |-1| = 1