已知y=log(1/2) [a^2x+2(ab)^x-b^2x+1] (a.b∈R+),求使y为负值的x的取值范围已知y=log1/2[a^2x+2(ab)^x-b^2x+1] (a.b∈R+),求使y为负值的x的取值范围.
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已知y=log(1/2) [a^2x+2(ab)^x-b^2x+1] (a.b∈R+),求使y为负值的x的取值范围已知y=log1/2[a^2x+2(ab)^x-b^2x+1] (a.b∈R+),求使y为负值的x的取值范围.
已知y=log(1/2) [a^2x+2(ab)^x-b^2x+1] (a.b∈R+),求使y为负值的x的取值范围
已知y=log1/2[a^2x+2(ab)^x-b^2x+1] (a.b∈R+),求使y为负值的x的取值范围.
已知y=log(1/2) [a^2x+2(ab)^x-b^2x+1] (a.b∈R+),求使y为负值的x的取值范围已知y=log1/2[a^2x+2(ab)^x-b^2x+1] (a.b∈R+),求使y为负值的x的取值范围.
使y为负值,则:
a^2x+2(ab)^x-b^2x+1>1
a^(2x)+2a^x*b^x-b^(2x)>0
(a/b)^(2x)+2(a/b)^x-1>0
设(a/b)^x=t,
t^2+2t-1>0
t√2-1
因为t=(a/b)^x>0,
所以解是:t>√2-1
(a/b)^x>√2-1
1,如果a>b,
a/b>1
x>log(a/b) (√2-1)
2,如果a=b,
a/b=1
x∈R.
3,如果a
A-B
y=log1/2[a^2x+2(ab)^x-b^2x+1] < 0，则a^2x+2(ab)^x-b^2x+1>1 <=> a^2x+2(ab)^x-b^2x>0 =>[a^x+(-1+√2)b^x]*[a^x+(-1-√2)b^x]>0
显然a^x+(-1+√2)b^x 恒大于0 =>a^x+(-1-√2)b^x>0 =>a^x>(1+√2)b^x =>(a/b)^x > 1+√2
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y=log1/2[a^2x+2(ab)^x-b^2x+1] < 0，则a^2x+2(ab)^x-b^2x+1>1 <=> a^2x+2(ab)^x-b^2x>0 =>[a^x+(-1+√2)b^x]*[a^x+(-1-√2)b^x]>0
显然a^x+(-1+√2)b^x 恒大于0 =>a^x+(-1-√2)b^x>0 =>a^x>(1+√2)b^x =>(a/b)^x > 1+√2
取对数x*lg(a/b)>lg(1+√2)
1.a>b=>a/b>1=>lg(a/b)>0=>x>lg(1+√2)/lg(a/b) =>x>log(a/b)(1+√2)
2.a=b =>x*0>lg(1+√2)=>无解
3.a
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