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CDS 2023 · PYQ · Algebra · medium

If a² − bc = α, b² − ac = β, c² − ab = γ, then what is (aα + bβ + cγ)/((a+b+c)(α+β+γ)) equal to?

Answer

The correct answer is C: 1. Note that α+β+γ = a²+b²+c²−ab−bc−ca and aα+bβ+cγ = a³+b³+c³−3abc = (a+b+c)(a²+b²+c²−ab−bc−ca). Hence the ratio equals 1.

  1. A.a − b + c
  2. B.− a + b + c
  3. C.1✓ Correct
  4. D.a + b − c

Explanation

Note that α+β+γ = a²+b²+c²−ab−bc−ca and aα+bβ+cγ = a³+b³+c³−3abc = (a+b+c)(a²+b²+c²−ab−bc−ca). Hence the ratio equals 1.
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