Question

if a = √5+3/√5-3 and b = √5-3/√5+3, then find the value of a²+b²+ab​

Answer 1

Answer:

Hey there

So let's solve your your problem step by step.

We know that

(a+b)^2=a^2 + b^2 + 2ab.

So

We already have values for LHS as 5 and value of ab as 3.

So,

(a+b)^2 =5^2 = 25

And, 2ab = 2*3 = 6

Now we substitute the values for both in general equation and we get,

25 = a^2 + b^2 + 6

a^2 + b^2 = 25 -6 = 19.

Therefore, the answer to your question is 19.