Question

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Question number 15

Answer 1

Answer:

Step-by-step explanation:

y = √(p + 2q) + √(p - 2q) / √(p + 2q) - √(p - 2q)

//multiply  numerator and denominator with √(p + 2q) + √(p - 2q)

y = [√(p + 2q) + √(p - 2q)]² / p + 2q - p +2q

y = p + 2q + p -2q - 2√p² - 4q² / 4q

y =  p - √p² - 4q²/2q.

qy² - py + q = 0

q[p - √p² - 4q²/2q]² - p [p - √p² - 4q²/2q] + q

= q[p²+ p²- 4q² - 2p√p² - 4q²]/4q² - [ p²- p√p² - 4q²/2q] + q

= [p²+p²- 4q² - 2p√p² - 4q²]/4q - [ p² - p√p² - 4q²/2q] + q

=> 2p² - 4q² - 2p√p² - 4q² - 2p²+ 2p√p² - 4q² + 4q²

=> 0

Hence proved.