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Question

The sum of all distinct roots of the equation (x211x+29)(x28x+7)=1 is

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Solution

(x211x+29)(x28x+7)=1
Let a=x211x+29 and b=x28x+7

Case 1: ab=1 when a=1
x211x+29=1
x211x+28=0x=4,7

Case 2: ab=1 when b=0
x28x+7=0x=1,7

Case 3: ab=1 when a=1 and b is an even number.
x211x+29=1
x211x+30=0x=5,6
For x=5, LHS =(1)8=1=RHS
For x=6, LHS =(1)5=1RHS

Therefore, distinct roots are 1,4,5,7
Sum of distinct roots =4+7+1+5=17

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