Question

2√5 + √3 + 2√5 - √3. = a + √15b
________ ________
2√5 - √3 2√5 + √4


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Answer 1

Answer:

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Answer 2

Step-by-step explanation:

$\frac{2 \sqrt{5} + \sqrt{3} }{2 \sqrt{5} - \sqrt{3} } + \frac{2 \sqrt{5} - \sqrt{3} }{2 \sqrt{5} + \sqrt{3} } = a + \sqrt{15} b$

$\frac{2 \sqrt{5} + \sqrt{3} }{2 \sqrt{5} - \sqrt{3} } \times \frac{2 \sqrt{5} + \sqrt{3} }{2 \sqrt{5} + \sqrt{3} } + \frac{2 \sqrt{5} - \sqrt{3} }{2 \sqrt{5} + \sqrt{3} } \times \frac{2 \sqrt{5} - \sqrt{3} }{2 \sqrt{5} - \sqrt{3} }$

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

$\frac{20 + 3 + 2 \times 2 \sqrt{5} \times \sqrt{3} + 20 + 3 - 2 \times 2 \sqrt{5} \times \sqrt{3} }{20 - 3}$

$\frac{46}{17}$

$a = \frac{46}{17} and \: b = 0$

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