Question

if a and b are rational number and 2+root3 upon 2-root3 a+broot3 find the value of a and b

Answer 1

Heya !!!





2 + ✓3 / 2 - ✓3 = A + B✓8






LHS = 2+ ✓3 / 2 - ✓3




Rationalising the denominator 2-✓3




=> 2+✓3/2-✓3 × 2+ ✓3 / 2 + ✓3






=> ( 2 + ✓3)² / ( 2 - ✓3)( 2 + ✓3)





=> (2)² + (✓3)² + 2 ×2 ×✓3 / (2)² - (✓3)²





=> 4 + 3 + 4✓3 / 4-3





=> 7 + 4✓3 / 1





=> 7 + 4✓3





Now,





LHS = RHS




7 + 4✓3 = A + B✓3




Clearly,




A = 7 and B = 4



★ HOPE IT WILL HELP YOU ★