Question

√2 +2√3÷2√2+√3 = a +b√6.

Find the value of a and b.

Answer 1

Answer: a= -2/5 and b= 3/5

Step-by-step explanation:

√2 +2√3/(2√2+√3)= a +b√6.

On rationalisation LHS by 2√2-√3, we get,

(√2 +2√3)/(2√2+√3) × (2√2-√3)/ (2√2-√3) = a +b√6.

[(√2 +2√3) (2√2-√3)] / [(2√2)^2-(√3)^2]= a +b√6.

(4-√6+4√6-6) /(8-3) = a +b√6

(-2+3√6)/5 = a +b√6

(-2/5) +3√6/5 = a +b√6,

On comparing bitu sides, we get,

a= -2/5 and b= 3/5