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Milisia
@Milisia
August 2022
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Решите пожалуйста.
кореньх^4-9х^2+a^2=x^2+3x-a
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sedinalana
Verified answer
(√(x^4-9x²+a²))²=(x²+3x-a)²
x^4-9x²+a²=x^4+6x³-2x²a+9x²-6xa+a²
6x³+2x²(9-a)-6xa=0
2x(3x²+x(9-a)-3a)=0
x1=0
3x²+x(9-a)-3a=0
D=(9-a)²+36a=81-18a+a²+36a=(81+18a+a²)=(9+a)²>0⇒a∈(-∞;-9) U (-9;∞)
x2=(a-9-9-a)/6=-3
x3=((a-9+9+a)/6=a/3
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Answers & Comments
Verified answer
(√(x^4-9x²+a²))²=(x²+3x-a)²x^4-9x²+a²=x^4+6x³-2x²a+9x²-6xa+a²
6x³+2x²(9-a)-6xa=0
2x(3x²+x(9-a)-3a)=0
x1=0
3x²+x(9-a)-3a=0
D=(9-a)²+36a=81-18a+a²+36a=(81+18a+a²)=(9+a)²>0⇒a∈(-∞;-9) U (-9;∞)
x2=(a-9-9-a)/6=-3
x3=((a-9+9+a)/6=a/3