a+b3–√=12−3–√,a+b3=12−3,a + b\sqrt 3 = \frac{1}{{2 - \sqrt 3 }}{\text{,}} then a : b is equal to = ?" /> a+b3–√=12−3–√,a+b3=12−3,a + b\sqrt 3 = \frac{1}{{2 - \sqrt 3 }}{\text{,}} then a : b is equal to = ?" /> a+b3–√=12−3–√,a+b3=12−3,a + b\sqrt 3 = \frac{1}{{2 - \sqrt 3 }}{\text{,}} then a : b is equal to = ?" />

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If a and b are rational numbers and $a + b \sqrt{3} = \frac{1}{2 - \sqrt{3}},$ $a + b\sqrt 3 = \frac{1}{{2 - \sqrt 3 }}{\text{,}}$ then a : b is equal to = ?

12 : 1
22 : 3
3√3 : 1
4-√3 : 1

Answer:- 1

Explanation:-

Solution:

\begin{aligned} a + b \sqrt{3} = \frac{1}{2 - \sqrt{3}} \\ \Rightarrow \frac{1}{2 - \sqrt{3}} \times \frac{2 + \sqrt{3}}{2 - \sqrt{3}} \\ \Rightarrow \frac{2 + \sqrt{3}}{4 - 3} \\ \Rightarrow 2 + \sqrt{3} \end{aligned}

$\eqalign{ & a + b\sqrt 3 = \frac{1}{{2 - \sqrt 3 }} \cr & \Rightarrow \frac{1}{{2 - \sqrt 3 }} \times \frac{{2 + \sqrt 3 }}{{2 - \sqrt 3 }} \cr & \Rightarrow \frac{{2 + \sqrt 3 }}{{4 - 3}} \cr & \Rightarrow 2 + \sqrt 3 \cr}$ By rationalisation of denominator
⇒ a + b√3 = 2 + √3
⇒ Now compare the rational & irrational parts
∴ a = 2
b = 1
∴ a : b
2 : 1

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then a : b is equal to = ?", "text": "If a and b are rational numbers and

a + b \sqrt{3} = \frac{1}{2 - \sqrt{3}},

$a + b\sqrt 3 = \frac{1}{{2 - \sqrt 3 }}{\text{,}}$ then a : b is equal to = ?", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution: