Answer:
a = 29/46
b= - 9/46
Step-by-step explanation:
Given:
- (5 + 2√3)/(7 + √3) = a - √3b
Rationalizing the left side:
- (5+2√3)(7-√3)/(7+√3)(7-√3) =
- (35 + 14√3 - 5√3 - 2√3²)/(7² - √3²) =
- (35 - 6 + 9√3)/(49 - 3) =
- (29 + 9√3)/46 =
- 29/46 + √3 (9/46)
Comparing the left and right sides:
- a - √3b = 29/46 + √3 9/46
- a = 29/46
- b = - 9/46
