Question

What is the value of (a+b+c+d)^7 ?

Answer 1

5down votefavorite1Let aa and bb be the roots of the equation: x2−10cx−11d=0x2−10cx−11d=0 where cc and dd be the roots of x2−10ax−11b=0x2−10ax−11b=0. Find the value of a+b+c+da+b+c+d, assuming that they all are distinct.I first tried making an equation with roots (a+b)(a+b) and (c+d)(c+d) to get the sum of the roots, however I wasn't able to solve this question using that method as the answer which I got was in terms of the variables itself.I also tried placing aa into the first equation and cc into the second to cancel out a common term (−10ac−10ac), but after cancelling, I got: (a2−c2−11d+11b=0)(a2−c2−11d+11b=0). Now I don't know how to move ahead.