Question

If a/b = c/d prove that each of the given ratio is equal to `sqrt((3a^2 - 10c^2)/(3b^2 - 10d^2))`

Answer 1

Let `a/b = c/d = k`

Then a = bk and c = dk

`sqrt((3a^2 - 10c^2)/(3b^2 - 10d^2)) = sqrt((3(bk)^2 - 10(dk)^2)/(3b^2 - 10d^2)) = sqrt((k^2(3b^2 - 10d^2))/(3b^2 - 10d^2)) = k =  "each given ratio"`