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BYTMIN8
@BYTMIN8
March 2022
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 11 клас !
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hlopushinairina
A) 0.2^[(x²-3x-24)/x]≤0.04;⇒
0.2^[(x²-3x-24)/x]≤0.2²;⇒
(x²-3x-24)/x≤2;⇒ x²-3x-24≤2x;
x²-5x-24≤0;
x₁,₂=5/2⁺₋√(25/4 +24)=5/2⁺₋11/2;
x₁=8;x₂=-3;
-3≤x≤8;
б)3^(2x+1)+8·3^x-3≥0;⇒3·3^2x+8·3^x-3≥0;⇒
3^x=y;y>0;⇒3y²+8y-3≥0
3y²+8y-3=0;⇒y₁,₂=(-8⁺₋√(64+36)/6=(-8⁺₋10)/6;
y₁=-3;⇒3^x=-3-решения нет т.к 3^x>0;
y₂=1/3;
3^x=1/3;⇒x ≥ -1;
правая часть решается аналогично
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Answers & Comments
0.2^[(x²-3x-24)/x]≤0.2²;⇒
(x²-3x-24)/x≤2;⇒ x²-3x-24≤2x;
x²-5x-24≤0;
x₁,₂=5/2⁺₋√(25/4 +24)=5/2⁺₋11/2;
x₁=8;x₂=-3;
-3≤x≤8;
б)3^(2x+1)+8·3^x-3≥0;⇒3·3^2x+8·3^x-3≥0;⇒
3^x=y;y>0;⇒3y²+8y-3≥0
3y²+8y-3=0;⇒y₁,₂=(-8⁺₋√(64+36)/6=(-8⁺₋10)/6;
y₁=-3;⇒3^x=-3-решения нет т.к 3^x>0;
y₂=1/3;
3^x=1/3;⇒x ≥ -1;
правая часть решается аналогично