Question

find the value of a&b if :-

5+2√3/7+4√3= a+b√3​

Answer 1

Answer:

Multiply numerator and denominator by (7-4√3), we get

= \frac{(5+2\sqrt{3})(7-4\sqrt{3})}{(7+4\sqrt{3})(7-4\sqrt{3})}

= \frac{35-20\sqrt{3}+14\sqrt{3}-24}{7^{2}-\left(4\sqrt{3}\right)^{2}}

/* By algebraic identity:

(x+y)(x-y) = x²-y² */

=\frac{11-6\sqrt{3}}{49-48}

= 11-6\sqrt{3}--(1)

RHS = a-b\sqrt{3} --(2)\\(given)

Compare (1) and (2), we get

a = 11 , b = 6