please solve question no. 90..
it's
8^x +4^x +8^-x +4^-x+5
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hey, is it PACE booklet
are u in pace
it isnt booklet
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JALGAON
u ?
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f(x ) = 8^x + 4^x + 8^-x + 4^-x + 5
we know,
exponential term always positive so,
8^x , 4^x , 8^-x and 4^-x all are positive
so,
use ,
AM ≥ GM
( 8^x + 4^x + 8^-x + 4^-x )/4 ≥ ( 8^(x -x )×4^(x -x ) }^1/4 = 1
8^x + 4^x + 8^-x + 4^-x ≥ 4× 1 = 4
8^x + 4^x + 8^-x + 4^-x +5 ≥ 4 + 5 = 9
f (x ) ≥ 9
so, range € [ 9 , ∞ )
we know,
exponential term always positive so,
8^x , 4^x , 8^-x and 4^-x all are positive
so,
use ,
AM ≥ GM
( 8^x + 4^x + 8^-x + 4^-x )/4 ≥ ( 8^(x -x )×4^(x -x ) }^1/4 = 1
8^x + 4^x + 8^-x + 4^-x ≥ 4× 1 = 4
8^x + 4^x + 8^-x + 4^-x +5 ≥ 4 + 5 = 9
f (x ) ≥ 9
so, range € [ 9 , ∞ )
thank u very much u helped me a lot
pleasure ,
Excellent !
:-)
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