Question

√3-1 /√3+1
- Determine the rational numbers a and b if
√3+1 /√3-1
= a + √3b.​

Answer 1

Answer:

a= 2, b=-1

Step-by-step explanation:

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Answer 2

$\frac{ \sqrt{3} - 1 }{ \sqrt{3} + 1 } + \frac{ \sqrt{3} + 1}{ \sqrt{3} - 1 } = a + \sqrt{3} b \\ \\ \frac{( { \sqrt{3} - 1 })^{2} + ( { \sqrt{3} + 1 })^{2} }{3 - 1} = a + \sqrt{3} b \\ \\ \frac{2(3 + 1)}{2} = a + \sqrt{3} b \\ \\ 4 = a + \sqrt{3} b \\ \\ comparing \: \: both \: \: sides \\ a = 4 \: \: \: \: \: \: b = 0$