Question

what is the solution off 17

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Answer 1

Step-by-step explanation:

the rationalizing factor of

$\sqrt{3} + 1 \: \: \: is \: \: \sqrt{3 } - 1$

$= \frac{\sqrt{3} - 1}{ \sqrt{3} + 1 } \times \frac{ \sqrt{3} - 1}{ \sqrt{3} - 1 }$

$= \frac{( { \sqrt{3} - 1) }^{2} }{( { \sqrt{3}) }^{2} - ( {1})^{2} }$

$= \frac{ ({ \sqrt{3} )}^{2} + {1}^{2} - 2 \sqrt{3} }{3 - 1}$

$= \frac{3 + 1 - 2 \sqrt{3} }{2}$

$= \frac{4 - 2 \sqrt{3} }{2}$

$= 2 - \sqrt{3}$

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

$a = 2 \: \: \: \: \: \: \: b = - 1$