Question

Find the value of a and b.
√3+1/√3-1= a + b√3​

Answer 1

Answer:

a = 2 and b = 1

Step-by-step explanation:

$==: \frac{\sqrt{3} + 1 }{\sqrt{3} - 1 } = a + b\sqrt{3}\\==: \frac{\sqrt{3} + 1 }{\sqrt{3} - 1 } * \frac{\sqrt{3} + 1 }{\sqrt{3} + 1 } = a + b\sqrt{3}\\==: \frac{3 + 1 + 2\sqrt{3} }{3 - 1 } = a + b\sqrt{3}\\==: \frac{4 + 2\sqrt{3} }{2} = a + b\sqrt{3}\\==: 2 + \sqrt{3} = a + b\sqrt{3}$

a = 2 and b = 1

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Answer 2

Answer:

$\boxed{\bf .'. \ a=2,b=1}$

Step-by-step explanation:

$rationalising \ factor=\sqrt{3} +1 \\\\ => \frac{\sqrt{3}+1 }{\sqrt{3}-1 } \\\\ => \frac{\sqrt{3}+1 }{\sqrt{3}-1 } \times \frac{\sqrt{3}+1 }{\sqrt{3}+1 } \\\\ => \frac{(\sqrt{3}+1)(\sqrt{3} +1) }{(\sqrt{3}-1 )(\sqrt{3}+1)} \\\\ => \frac{\sqrt{3}^2+\sqrt{3}+\sqrt{3}+1^2}{\sqrt{3}^2-1^2} \\\\ => \frac{3+1+2\sqrt{3}}{3-1} \\\\ => \frac{4+2\sqrt{3}}{2} \\\\ =>2+\sqrt{3} =a+b\sqrt{3} \\\\ \boxed{.'. \ a=2,b=1} \\\\ ------------------ \\ formula \ used: \\ (a+b)(a-b)=a^2-b^2 \\ ------------------$