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2023

Mathematics

JAMB

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 = −5
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