Question

if a = 2-√5 / 2+√5 and b =2+√5/2-√5, find a 2 - b 2.

Answer 1

Answer:

-144√5

Step-by-step explanation:

Solution:-

a = (2-√5)/(2+√5) and b = (2+√5)/(2-√5)

a = (2-√5)/(2+√5) × (2-√5)/(2-√5)

⇒ (4-4√5+5)/(4-5)

⇒ (9-4√5)/-1

⇒ a = -9+4√5

b = (2+√5)/(2-√5) × (2+√5)/(2+√5)

⇒ (4+4√5+5)/(4-5)

⇒ (9+4√5)/-1

b = -9-4√5

a² - b² = (-9+4√5)² - (-9-4√5)

⇒ 81+80-72√5 - (81+80+72√5)

⇒ 81+80-72√5-81-80-72√5

⇒ -72√5-72√5

a² - b² = -144√5  Answer.

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