if a and b are rational numbers and 2+√3/2-√3=a+b√3 find a and b​

2 thoughts on “if a and b are rational numbers and 2+√3/2-√3=a+b√3 find a and b​”

1. Answer:

   Step-by-step explanation:

   2+root3/2-root 3

   =2+[tex]\sqrt{3\\[/tex]/2-[tex]\sqrt{3\\[/tex] * 2+[tex]\sqrt{3\\[/tex]/2-[tex]\sqrt{3\\[/tex]

   =(2+[tex]\sqrt{3\\[/tex])^2/ 2^2 – ([tex]\sqrt{3\\[/tex])^2

   4+3+4[tex]\sqrt{3\\[/tex]/4-3

   7+4[tex]\sqrt{3\\[/tex]/1

   On comparing

   a+b[tex]\sqrt{3\\[/tex] = 7+4[tex]\sqrt{3\\[/tex]

   Hence a = 7

   b = 4

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2. Answer:

   a=7

   b=4

   Step-by-step explanation:

   [tex] \frac{2 + \sqrt{3} }{2 – \sqrt{3} } \\ = \frac{2 + \sqrt{3} }{2 – \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ = \frac{4 +4 \sqrt{3} + 3 }{4 – 3} \\ = \frac{7 + 4 \sqrt{3} }{1} \\ = 7 + 4 \sqrt{3} \\ a + b \sqrt{3} = 7 + 4 \sqrt{3} \\ a = 7 \\ b = 4[/tex]

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