Question

Value of (√3-1)/√3+1=a+b√3

Answer 1

Answer:

a = 2, b = - 1

Step-by-step explanation:

(√3 - 1)/ (√3 + 1) = a + b√3

or, {(√3 -1) × (√3 - 1)}/ { (√3 +1) × (√3 - 1) = a + b√3

[ Using the identity--:

[ Using the identity--:(a - b)² = a² - 2ab +b²

[ Using the identity--:(a - b)² = a² - 2ab +b²a² - b² = (a +b) (a- b) ]

or, (√3 -1)² / 2 = a + b √3

or, { 3 - 2 √3 + 1} / 2 = a + b √3

or, (4- 2√3) /2 = a + b√3

or, 2(2 - √3) / 2 = a + b √3

[ Cancelling, the common factor 2 ]

or, 2 - √3 = a + b √3

or, 2 + (-1) √3 = a + b√3 ............(1)

Comparing both sides we get,

a = 2 , b = - 1 ANS

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