Question

If a and b are rational numbers and 5+2√3/7+4√3=a-b√3

Answer 1

5+2√3 / 7+4√3

Multiplying both numerator and the denominator with 7-4√3 ,i.e., rationalising the denominator.

We get,

(5+2√3 / 7+4√3)*(7-4√3 / 7-4√3)

= (5+2√3)(7-4√3) / (7+4√3)(7-4√3)

= (35-20√3+14√3-24) / (7^2 - (4√3)^2)

{By the formula (a+b)(a-b) = (a^2 - b^2)}

= (9-6√3) / (49-48)

= (9-6√3) / 1

= 9-6√3

Since,

9-6√3 = a-b√3

Therefore,

a=9

b =6