If 2+32−3=a+b3 , then the value of (a,b) is

2+32−3=(2+3)24−3 =4+3+43 =7+43 ∴a=7,b=4

If 2+32−3=a+b3 , then the value of (a,b) is

2+32−3=(2+3)24−3 =4+3+43 =7+43 ∴a=7,b=4

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If $\frac{2 + \sqrt{3}}{2 - \sqrt{3}} = a + b \sqrt{3}$ , then the value of $(a, b)$ is

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(7, - 4)

(- 7, - 4)

(7, 4)

(7, 2)

answer is B.

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Detailed Solution

\frac{2 + \sqrt{3}}{2 - \sqrt{3}} = \frac{{(2 + \sqrt{3})}^{2}}{4 - 3}

$= 4 + 3 + 4 \sqrt{3}$

$= 7 + 4 \sqrt{3}$

$∴ a = 7, b = 4$

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If 2+32−3=a+b3 , then the value of (a,b) is

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If $\frac{2 + \sqrt{3}}{2 - \sqrt{3}} = a + b \sqrt{3}$ , then the value of $(a, b)$ is