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If (ax + b)(bx + a) = 26x^2 + v * x + 26, where a,b , and v are distinct integers, what is the minimum possible value of v, the coefficient of x?

 Jun 26, 2018
 #1
avatar+101344 
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(ax + b) ( bx + a)  =  ab x^2  +  ( a^2 + b^2) x  +  ab

 

So..equating coefficients, then  ab  = 26   and  a^2 + b^2  = v

 

If  ab   = 26   and a,b are distinct intergers....then we have the following possibilities for a,b

 

a         b             a^2  +  b^2

26       1             26^2 + 1^2  =  677

13       2             13^2  + 2^2  = 173

 

So...the minimum value for v  =  173

 

 

 

cool cool cool

 Jun 26, 2018

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