If 0
Question
If 0<x<π and the expression that exp{(1+|cosx|+cos^2x+∣∣cos^3x∣∣+cos^4x+….. upto∞)log_e 4} satisfies the quadratic equation y^2 20y+64=0 the find the value of x
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If (0 < x < pi ) and the expression that ( exp left{left(1+|cos x|+cos ^{2} x+left|cos ^{3} xright|+cos ^{4} x+ldots . .right.right. )
(upto left.infty) log _{mathrm{e}} 4right} ) satisfies the quadratic equation ( y^{2} ) ( quad 20 y+64=0 ) the find the value of ( x )

JEE/Engineering Exams
Maths
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If 0<x<π and the expression that exp{(1+|cosx|+cos^2x+∣∣cos^3x∣∣+cos^4x+….. upto∞)log_e 4} satisfies the quadratic equation y^2 20y+64=0 the find the value of x
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( 1+|cos x|+cos ^{2} x+cdots )
loge ( =e^{frac{log _{e} 4}{|-| cos x mid}} cdot log _{e} d theta )
( y^{2}-20 y+64=0 )
( y^{2}-16 y-4 y+64=0 )
( (y-16)(y-4)=0 )
( y=4,16 )
( Rightarrow e^{frac{log _{e} 4}{1-log x}}=4,16 )
( Rightarrow frac{log _{e} 4}{1-|cos x|}=log _{e} 4 ) or ( 2 log _{e} 4 )
( Rightarrow quad 1-|cos x|=1 quad ) OR ( quad|-| cos x mid=frac{1}{2} )
( Rightarrow|cos x|=0 quad ) OR ( quad|cos x|=frac{1}{2} )
( quad  Rightarrow quad x=frac{pi}{2}- ) OR ( quad x=frac{pi}{3} )

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