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MATHEMATICS

JAMB 2001 - Question 5

Mathematics 2001 JAMB Past Questions - Question 5: Given that p=1+√2 and q = 1 -;√2, evaluate P²-q²/2pq

Given that p=1+√2 and q = 1 -;√2, evaluate P²-q²/2pq

A: -2(2+√2)

B: 2(2+√2)

C: -2√2

D: 2 √2

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Correct Answer

Explanation

To evaluate the expression (p² - q²) / (2pq), we need to substitute the values of p and q into the expression and simplify it.Given:p = 1 + √2q = 1 - √2Let's substitute these values into the expression:(p² - q²) / (2pq) = (p+q)(p-q)/2pq (1 + 2√2 - (1 - √ 2))(1 + √ 2 + 1 - √ 2) ((1 + √2)² - (1 - √2)²) / (2(1 + √2)(1 - √2)) = (1 + 2√2 + (√2)² - (1 - 2√2 + (√2)²)) / (2(1 + √2)(1 - √2)) (2√2)(2) / (-2) -2√2