Question

Can i get this answer explained

Answer 1

Answer:

hey mate here is your answer

hope u understand it

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Answer 2

Question:

Find the value of a and b, if $\dfrac{2 - \sqrt{3}}{2 + \sqrt{3}} = a + b\sqrt{3}$

Answer:

$\boxed{<strong> </strong>a = 7}$

$\boxed{b = -4}$

Step By Step Solution:

$\dfrac{2 - \sqrt{3}}{2 + \sqrt{3}} = a + b\sqrt{3}$

Rationalizing the denominator

$= \dfrac{2 - \sqrt{3}}{2 + \sqrt{3}} \times \dfrac{2-\sqrt{3}}{2-\sqrt{3}} = a + b\sqrt{3}$

$= \dfrac{{(2-\sqrt{3})}^{2}}{{(2)}^{2} - {(\sqrt{3})}^{2}} = a + b\sqrt{3}$

$= \dfrac{{(2-\sqrt{3})}^{2}}{4 - 3} = a + b\sqrt{3}$

$= \dfrac{({2-\sqrt{3})}^{2}}{1} = a + b\sqrt{3}$

$= 4 + 3 - 2(2)(\sqrt{3}) = a + b\sqrt{3}$

$= 7 - 4\sqrt{3} = a + b\sqrt{3}$

On comparing

a = 7

b = -4

☆Identities used☆

• $a^{2} - b^{2} = (a + b)(a - b)$

• ${(a - b)}^{2} = a^{2} + b^{2} - 2ab$