Question

if 5+√3/5-√3=a+b√3 find a and hence find(a+b)2​

Answer 1

Answer:

can you tell me the answer in comment

Answer 2

Answer:

The value of 'a' is 14 / 11 and the value of 2(a+b) is 38 / 11

Step-by-step explanation:

It is given that 5+√3 / 5-√3 is equal to a+b√3

First, let us simply simplify the LHS of the given equation.....

On rationalising LHS, we get (5+√3)² / 22 which is equal to 28+10√3 / 22

Now, we know that 28+√3 / 22 can be written as (28 / 22) + (10√3 / 22)

That can be further simplified as (14 / 11) + (√3)(5 / 11)

Now, we simplified the LHS and if we observe, LHS is quiet similar to RHS, i.e., a=(14 / 11) and b=(5 / 11)

As we now got the values of 'a' and 'b', we can find out what ever is asked in the question.

Hope this helps you.