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MATHEMATICS

JAMB 2011 - Question 8

Mathematics 2011 JAMB Past Questions - Question 8: Rationalize 2- √5 /3-√5

Rationalize 2- √5 /3-√5

A: 1 - √5/2

B: 1- √5/4

C: √ 5-1/2

D: 1+√ 5/4

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Correct Answer

Explanation

2- √5 /3-√5(2- √5)(3-√5)/(3-√5)(3 + √5)=6 + 2 √5 – 3 √5 -5 /9- 5 = 6-5-√5 /4= 1-√5/4To rationalize the expression (2 - √5) / (3 - √5), we can multiply the numerator and denominator by the conjugate of the denominator, which is (3 + √5):[(2 - √5) / (3 - √5)] * [(3 + √5) / (3 + √5)]Expanding the numerator and denominator:[(2 * 3) + (2 * √5) - (√5 * 3) - (√5 * √5)] / [(3 * 3) + (3 * √5) - (√5 * 3) - (√5 * √5)]Simplifying:[6 + 2√5 - 3√5 - 5] / [9 + 3√5 - 3√5 - 5]Combining like terms:[1 - √5] / [4]Therefore, the rationalized form of (2 - √5) / (3 - √5) is (1 - √5) / 4.