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makslavrov94
@makslavrov94
August 2021
1
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Решите неравенство:
9^(x-2) -37*3^(x-3) +30 меньше или равно 0.
^- степень
*-умножить
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sedinalana
Verified answer
1/81*9^x-37/27*3^x+30≤0
9^x-111^3^x+2430≤0
3^x=a
a²-111a+2430≤0
a1+a2=111 U a1*a2=2430
a1=30 U a2=81
30≤a≤81⇒30≤3^x≤81⇒1+log(3)10≤x≤4
x∈[1+log(3)10;4]
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Verified answer
1/81*9^x-37/27*3^x+30≤09^x-111^3^x+2430≤0
3^x=a
a²-111a+2430≤0
a1+a2=111 U a1*a2=2430
a1=30 U a2=81
30≤a≤81⇒30≤3^x≤81⇒1+log(3)10≤x≤4
x∈[1+log(3)10;4]