Question

ifa=6+2√3 find a-1/a

Answer 1

Heya !!!





A = 6 + 2✓3




1/A = 1/6+2✓3



Rationalizing the denominator 6+2✓3



1/A = 1/6+2✓3 × 6-2✓3/6-2✓3





1/A = (6-2✓3)/( 6+2✓3)(6-2✓3)




1/A = (6-2✓3)/(6)² - (2✓3)²



1/A = (6-2✓3)/36-12




1/A = (6-2✓3)/24




1/A = 2(3-✓3)/24 = 3-✓3/12






Now,




A - 1/A = 6+2✓3 - (3-✓3)/12









=> 12(6+2✓3) - ( 3-✓3)/12






=> 72 + 24✓3 - 3 + ✓3 / 12





=> 69 + 25✓3/12







HOPE IT WILL HELP YOU...... :-)