Question

Solve the following . Find

Answer 1

Step-by-step explanation:

I

t h i n k

t h i s

is

t h e

a n s

c h e c k

t h i s

Answer 2

Answer:

♦ a = 29/46

♦ b = - 9/46

Step-by-step explanation:

$\sf \implies \: \dfrac{5 - 2 \sqrt{3} } {7 - \sqrt{3} } = a + \sqrt{3} b$

$\\ \sf \implies \: \dfrac{5 - 2 \sqrt{3} \: \times 7 + \sqrt{3} } {7 - \sqrt{3} \times 7 + \sqrt{3}} = a + \sqrt{3} b$

$\\ \sf \implies \: \dfrac{35 + 5 \sqrt{3} - 14 \sqrt{3} - 2 \times 3 }{ {7}^{2} - { (\sqrt{3}) }^{2} } = a + \sqrt{3} b$

$\\ \sf \implies \: \dfrac{35 + 5 \sqrt{3} - 14 \sqrt{3} - 6}{ 49 - 3 } = a + \sqrt{3} b$

$\\ \sf \implies \: \dfrac{35 + 5 \sqrt{3} - 14 \sqrt{3} - 6}{ 46 } = a + \sqrt{3} b$

$\\ \sf \implies \: \dfrac{29 - 9 \sqrt{3}}{ 46 } = a + \sqrt{3} b$

$\\ \sf \implies \: \dfrac{1}{ 46 }( 29 - 9 \sqrt{3}) \: = a + \sqrt{3} b$

$\\ \sf \implies \: ( \frac{29}{46} - \frac{9\sqrt{3}}{46}) \: = a + \sqrt{3} b$

Therefore,

$\\ \sf \leadsto \: a = \dfrac{29}{46}$

$\\ \sf \leadsto \: b = - \dfrac{9}{46}$

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