If a:b = c:d prove that ac/bd = a^2 - 3c^2/ b^ 2 - 3d^2
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Step-by-step explanation:
ad=bc
a=bc/d
LHS=AC/bd
=(bc/d)*(c/bd)
= (bc^2)/(bd^2)
=c^2/d^2 ------------------(1)
RHS= a^2-3c^2/b^2-3d^2
=(bc/d)^2-3c^2 / b^2-3d^2
= (b^2c^2-3c^2 d^2)/ (b^2-3d^2)d^2
= c^2(b^2- 3d^2)/(b^2-3d^2)d^2
= c^2/ d^2 --------------- (2)
Thus LHS=RHS
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