Unique Quadrata
Algebra
Level
4
are distinct numbers such that:
- and are the roots of the equation
- and are the roots of the equation
Find the value of .
The answer is 30.
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1 solution
a + b = 2 c , c + d = 2 a , a b = − 5 d , c d = − 5 b
Therefore a c = 2 5 , a + c = b + d
Thus req. value is 2 ( a + c )
Satisfying a and c in respective quadratic equations , and adding resultant quads, we get a quad in (a+c).
Equations give value of a+c= 1 5 a n d − 2 0 .
Answer follows after that.