Question

if A-Broot3=2-root3/2+root3 then find value of a and b​

Answer 1

Answer:

Step-by-step explanation:

Given :

$A-B\sqrt{3} = \frac{2-\sqrt{3} }{2+\sqrt{3} }$

To Find :

The values of A & B,.

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To find A & B,

initially, we shall simplify the given RHS (Right-Hand-Side), by taking conjugate $\frac{2-\sqrt{3} }{2+\sqrt{3} }  = \frac{2-\sqrt{3} }{2+\sqrt{3} } X \frac{2-\sqrt{3} }{2-\sqrt{3} } = \frac{(2-\sqrt{3})^2 }{(2+\sqrt{3})(2-\sqrt{3})  }$

Applying the algebraic formulas,

( a - b )² = a² - 2ab + b²

and,

( a + b )( a - b ) = a² - b²

where a = 2 & b = √3

⇒ $\frac{(2)^2 - 2(2)(\sqrt{3}) + (\sqrt{3})^2  }{2^2 - (\sqrt{3})^2 }$

⇒ $\frac{4 + 3 - 4\sqrt{3} }{4 - 3}$

⇒ $\frac{7 - 4\sqrt{3} }{1}=7-4\sqrt{3}$

Hence,

∴ $\frac{2-\sqrt{3} }{2+ \sqrt{3} } = 7 - 4\sqrt{3}$

⇒ $A - B\sqrt{3} = 7 - 4\sqrt{3}$

⇒ $A = 7,$

⇒$-B\sqrt{3} = -4\sqrt{3}$

Dividing both the sides by $-\sqrt{3}$ ,

We get,

⇒ $\frac{-B\sqrt{3} }{-\sqrt{3} } = \frac{-4\sqrt{3} }{-\sqrt{3} }$

⇒ $B = 4$

∴ A = 7,

∴ B = 4

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Answer 2

$\huge {\bold {\red {s0lUtion}}}$

➖ ➖ ➖ ➖ ➖ ➖ ➖ ➖ ➖
a = 7
b = 4
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$\bold \blue {{HOPE \: YOU \: GOT \: IT}}$