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penek1
@penek1
August 2022
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5^x+5^y=30
x+y=3
система
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ShirokovP
Verified answer
X = 3 - y
5^(3 - y) + 5^y = 30 *
125/5^y + 5^y - 30 = 0
Пусть 5^y = t
125/t + t - 30 = 0
t^2 - 30t + 125 = 0
D = 900 - 500 = 400
t₁ = ( 30 + 20)/2 = 25;
t₂ = ( 30 - 20)/2 = 5;
5^y = 25
y₁ = 2
5^y = 5
y₂ = 1
x₁ = 1
y₁ = 2
x₂ = 2
y₂ = 1
Ответ
( 1; 2) ; (2; 1)
3 votes
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Answers & Comments
Verified answer
X = 3 - y5^(3 - y) + 5^y = 30 *
125/5^y + 5^y - 30 = 0
Пусть 5^y = t
125/t + t - 30 = 0
t^2 - 30t + 125 = 0
D = 900 - 500 = 400
t₁ = ( 30 + 20)/2 = 25;
t₂ = ( 30 - 20)/2 = 5;
5^y = 25
y₁ = 2
5^y = 5
y₂ = 1
x₁ = 1
y₁ = 2
x₂ = 2
y₂ = 1
Ответ
( 1; 2) ; (2; 1)