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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: Functions
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rahulraj1 (14)

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sin(eX)=2X+2-x  then find the number of real solutions?
    
akhil_o (2709)

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RHS minimum value=2 at x=0
LHS max value=1
so no solution

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anandghegde (1712)

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\text{By AM GM, we get}\\ \\ \frac{2^{x}+2^{-x}}{2} \ge \sqrt{2^{x}.2^{-x}}\\ \\ 2^{x}+2^{-x} \ge 2\\ \\  \text{RHS is always greater than or equal to 2, but LHS is always less than or equal to 1. Hence no solution}

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anandghegde (1712)

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oh sorry akhil....dint know you were at it.

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ankitagg (330)

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no solution because sin(eX) has the range from [-1,1]
whereas 
2X+2-x  has the least value of 2.

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