If (frac{a}{c}) = (frac{c}{d}) = k, find the value of (frac{3a^2 – ac + c^2}{3b^2 – bd + d^2})
-
A.
3k2 -
B.
2k – k2 -
C.
(frac{3b^2k^2 – bk^2d + dk^2}{3b^2 – bd + d^2}) -
D.
k2
Correct Answer: Option C
Explanation
(frac{a}{c}) = (frac{c}{d}) = k
∴ (frac{a}{b}) = bk
(frac{c}{d}) = k
∴ c = dk
= (frac{3a^2 – ac + c^2}{3b^2 – bd + d^2})
= (frac{3(bk)^2 – (bk)(dk) + dk^2}{3b^2 – bd + a^2})
= (frac{3b^2k^2 – bk^2d + dk^2}{3b^2 – bd + d^2})
k = (frac{3b^2k^2 – bk^2d + dk^2}{3b^2 – bd + d^2})