Find the values of a and b
if 5+2√37+4√3=a+b√3
a=11,b=−6
5+2√37+4√3can be simplified by rationalizing the denominator (7+4√3). We can rationalize the given denominator by multiplying the given number (7+4√3)with its rationalizing factor (7−4√3).
Multiplying the numerator and denominator with (7−4√3), we get
(5+2√3)(7−4√3)(7+4√3)(7−4√3)=35+14√3−20√3−8(√3√3)(7)(7)−(4×4)(√3×√3)
=35−6√3−2449−48
=11−6√3
On comparing, with a+b√3, we get a=11,b=−6