Q.

Solution set of 2x(2x+1+8)8x(52x) is [α,β] then βα is ___

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answer is 1.

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Detailed Solution

 2x(2.2x+8)23x(52x)t(2t+8)t3(5t)(bytaking2x=t)
 2t2+8t5t3t4
 2t+85t2t3
 t35t2+2t+80
Roots are 1,2,4 
(t+1)(t2)(t4)0t(,1][2,4]2x[2,4]x[1,2]

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