Question

find the value of a and b ,a-b√3=4-2√3/5+3√3

Answer 1

The answer is :-

$a = ( - 19) \\ b = ( - 11)$
The first and foremost step was rationalization.

The step gave us the simplified form of the RHS.

Now,
Consider an example :-

If 3x + 4 = 33 + 4
What will be x?

Answer is x = 11
How?
3x = 33 +4 - 4 = 33
So, x = 33/3 = 11

Similarly,
In the above question, we got

a - b root3 = (-19) + 11 root3
So,
a should be equal to (-19) to satisfy the equation as the value of the only constant in the equation is (-19)

Similarly,
b will be (-11) as if we put (-11) in the LHS we get that (-) *(-) gives a (+) sign for b.
The b has a (+) sign in the RHS.

Thus, it was to satisfy the equation.


The answer is derived simply by rationalizing the given terms and equating.