If a and b are of the same sign and $$(3a^2-8b^2):(a^2+4b^2)= 2:1$$​, then a : b = ?

Correct option is D

Given:

​$$(3a^2 - 8b^2) : (a^2 + 4b^2) = 2 : 1$$​

We need to find the value of a : b.

Solution:

​$$\frac{3a^2 - 8b^2}{a^2 + 4b^2} = \frac{2}{1}$$​​

​$$3a^2 - 8b^2 = 2(a^2 + 4b^2)$$​

​$$3a^2 - 2a^2 = 8b^2 + 8b^2$$​

​$$a^2 = 16b^2$$​

a = 4b

Since a and b are of the same sign, we have:

a : b = 4 : 1