2023
Mathematics
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If (3−√3)/(2+√3) = a + b√3, what are the values a and b?
A.
a = 9, b = -5
B.
a = 5, b = 9
C.
a = 9, b = 5
D.
a = -5, b = 9
Correct Answer: a = 9, b = -5
Explanation
(3−√3)/(2+√3) = a + b√3 Rationalize = (3 − √3)/(2+√3) × (2−√3)/(2−√3) = (3−√3)/(2+√3)(2−√3)/(2−√3) = 6−3√3−2√3+(√3)2/4−2√3 + 2√3 − (√3)2 = (6−5√3+3)/(4−3) = (9−5√3)/1 = 9 − 5√3 = 9 + (-5)√3 ∴a= 9, b = −5
(3−√3)/(2+√3) = a + b√3 Rationalize = (3 − √3)/(2+√3) × (2−√3)/(2−√3) = (3−√3)/(2+√3)(2−√3)/(2−√3) = 6−3√3−2√3+(√3)2/4−2√3 + 2√3 − (√3)2 = (6−5√3+3)/(4−3) = (9−5√3)/1 = 9 − 5√3 = 9 + (-5)√3 ∴a= 9, b = −5THIS WEEK's
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