Question

If a:b = c:d prove that ac/bd = a^2 - 3c^2/ b^ 2 - 3d^2​

Answer 1

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