1Using the relations 2-5x-3x2>0 and x2-4x-11>0, I get x to be (-2,2-√15). log11(x2-4x-11) is not defined for x=2-√15.
However are these results enough to satisfy the relation
log5(x2-4x+11)2 ≥ log11(x2-4x-11)3 ??
Tell me, how to proceed with this one -
Solve the inequality :
log5(x2-4x+11)2-log11(x2-4x-11)3√2-5x-3x2≥0
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5 Answers
62for this, note that the Denominoator is always positive..
numerator needs to be +ve
also you need the denominator to be defined
so 2-5x-3x2>0
Using these can you proceed?
1
11One nice way is to take x2-4x+11=k, then x2-4x-11=k-22.
From which we have k2≥(k-22)2
Hence for all k for which the exp is defined, it shall satisfy the inequality.
62Mayukh, there is a bit more..
for instance, (x2-4x+11) need not be +ve... because it is being squared before taking log....
the only other thing you need to take care of is that (x2-4x-11)>0