Question

If 5+√3 / 5-√3 = a +b √3, find a & b.

Answer 1

Answer:

here is your answer

Step-by-step explanation:

The value of (a+b)a is 20. On comparing both sides. Therefore the value of (a+b)a is 20.

Answer 2

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If 5+√3 / 5-√3 = a +b √3, find a & b.

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$\huge\sf\underline{Answer:}$

$\small\fbox\pink{˙❥(a+b)²=a²+b²+2ab}$

$\small\fbox\pink{˙❥(a)²-(b)²=(a+b)(a-b)}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{5 + \sqrt{3} }{5 - \sqrt{3} }$

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$\\ \: \: \: \frac{5 + \sqrt{3} }{5 - \sqrt{3} } \: \: \times \: \: \frac{5 + \sqrt{3} }{5 + \sqrt{3} }$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{(5 + \sqrt{3}) {}^{2} }{5 {}^{2} - ( \sqrt{3) {}^{2} } }$

$\\ \: \: \: \: \frac{(5) {}^{2} + ( \sqrt{3} ) {}^{2} + 2(5 \times \sqrt{3} )}{(5) {}^{2} - ( \sqrt{3} ) {}^{2} } \: \: \:$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{25 + 3 +2(5 \sqrt{3} )}{22}$

$\\ \\ \ \: \: \: \: \: \: \: \: \: \: \: \: \frac{25 + 3 + 10 \sqrt{3} }{22}$

$\\ \: \: \: \: \: \: \: \: \: \: \: \:\:\: \: \: \frac{28 + 10 \sqrt{3} }{22}$

$\\ \\ \:\: \: \: \: \: ⟼\frac{14 + 5 \sqrt{3} }{11}$

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$\small\mathfrak\pink{hence,a = \frac{14}{11} \: and \: b = \frac{5 \sqrt{3} }{11} }{}$

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$\Large\purple{\textbf {\textsf {@akeertana503}}}$