Question

If a-b√3 = 2-√3/2+√3, find the value of a and b

Answer 1

Step-by-step explanation:

a - b√3

= ( 2-√3)/(2+√3)

= [(2-√3)(2-√3)]/[(2+√3)(2-√3)]

= (2-√3)²/[2²-(√3)²]

= [2²-2×2×√3+(√3)²]/(4-3)

= 4 - 4√3 + 3

= 7 - 4√3

Therefore ,

a - b√3 = 7 - 4√3

a = 7 , b = 4

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Answer 2

2-√3 / 2+√3

multiply 2-√3 to the numerator and denominator

(2-√3)(2-√3) / (2+√3)(2-√3)

(4+3-4√3) / (4-3)

(7-4√3) / 1

7-4√3.............(1)

Given equation is

a-b√3..............(2)

Equating equation (1) and (2), we get

a = 7 and b = 4

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