Question

If a, b, c and d are in proportion, the value of `(8a^2 - 5b^2)/(8c^2 - 5d^2)` is equal to ______.

Options

• a² : b²

• a² : c²

• a² : d²

• c² : d²

Answer 1

If a, b, c and d are in proportion, the value of `(8a^2 - 5b^2)/(8c^2 - 5d^2)` is equal to a² : c².

Explanation:

Since a, b, c and d are in proportion

∴ a : b :: c : d

`\implies a/b = c/d = k`  ...(Say)

`\implies` a = bk and c = dk

`(8a^2 - 5b^2)/(8c^2 - 5d^2) = (8b^2k^2 - 5b^2)/(8d^2k^2 - 5d^2)`

= `(b^2(8k^2 - 5))/(d^2(8k^2 - 5))`

= `b^2/d^2`

= `(a/k)^2/(c/k)^2`

= `(a^2/k^2)/(c^2/k^2)`

= `a^2/c^2`