Question

find the value of a and b if √3-1/√3+1=a+b√3​

Answer 1

given :- (√3 - 1)/(√3 + 1) = a + b√3

LHS :-

= (√3 - 1)/(√3 + 1) × (√3 - 1)/(√3 - 1)

= (√3 - 1)²/[(√3 + 1)(√3 - 1)]

= [(√3)² - 2(√3)(1) + (1)²]/[(√3)² - (1)²]

= (3 - 2√3 + 1)/(3 - 1)

= (4 - 2√3)/2

= 2 - √3

RHS :-

a + b√3

comparing LHS with RHS we get,

➡ 2 - √3 = a + b√3

therefore a = 2 and b = -1

Answer 2

Answer:-

According to the given question:-

(√3 - 1)/(√3 + 1) = a + b√3

Left hand side

= (√3 - 1)/(√3 + 1) × (√3 - 1)/(√3 - 1)

= (√3 - 1)²/(√3 + 1)(√3 - 1)

= (√3)² - 2(√3)(1) + (1)²]/[(√3)² - (1)²

= (3 - 2√3 + 1)/(3 - 1)

= (4 - 2√3)/2

= 2 - √3

Right hand side

a + b√3

2 - √3 = a + b√3

Hence, a = 2 and b = -1