Question

find p and q if $\implies \dfrac{7 + \sqrt{5} }{7 - \sqrt{5} } - \dfrac{7 - \sqrt{5} }{7 + \sqrt{5} } = p - 7\sqrt{5} q$​

Answer 1

$\circledcirc\mathtt\blue{ \: Question:-}$

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$\blue\Rsh \tt{ \frac{7 + \sqrt{5} }{7 - \sqrt{5} } - \frac{7 - \sqrt{5} }{7 + \sqrt{5} } = } \small \tt \blue{ \: p - 7 \sqrt{5}q }$

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$\circledcirc\mathtt\blue{ \: Solution:-}$

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$\blue\Rsh \tt{ \frac{7 + \sqrt{5} }{7 - \sqrt{5} } - \frac{7 - \sqrt{5} }{7 + \sqrt{5} } = } \small \tt \blue{ \: p - 7 \sqrt{5}q }$

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$\Rsh\small\mathtt\blue{Rationalise \: the \: denominator}$

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$\blue\Rsh \tt{ \frac{7 + \sqrt{5} }{7 - \sqrt{5} } \times \frac{7 + \sqrt{5} }{7 + \sqrt{5} } - \frac{7 - \sqrt{5} }{7 + \sqrt{5} } \times \frac{7 - \sqrt{5} }{7 - \sqrt{5} } = } \small \tt \blue{ \: p - 7 \sqrt{5} }$

$\blue\Rsh \tt{ \frac{(7 + \sqrt{5}) ^{2} }{ {(7)}^{2} - (\sqrt{5})^{2} } - \frac{(7 - \sqrt{5})^{2} }{ {(7)}^{2} - (\sqrt{5})^{2} } = } \small \tt \blue{ \: p - 7 \sqrt{5}q }$

$\blue\Rsh \tt{ \frac{ (7)^{2} +2 \times 7 \times \sqrt{5} + 5 }{ 49- 5 } - \frac{((7)^{2} - 2 \times 7 \times \sqrt{5} + (\sqrt{5})^{2} )}{ 49 - 5 } = } \small \tt \blue{ \: p - 7 \sqrt{5}q }$

$\blue\Rsh \tt{ \frac{ 49 + 14 \sqrt{5} + 5 }{ 44 } - \frac{(49 - 14 \sqrt{5} + 5 ) }{ 44 } = } \small \tt \blue{ \: p - 7 \sqrt{5}q }$

$\blue\Rsh \tt{ \frac{ 54 + 14 \sqrt{5} }{ 44 } - \frac{(54 - 14 \sqrt{5} ) }{ 44 } = } \small \tt \blue{ \: p - 7 \sqrt{5} }$

$\blue\Rsh \tt{ \frac{ 54 + 14 \sqrt{5} }{ 44 } - \frac{54 + 14 \sqrt{5} }{ 44 } = } \small \tt \blue{ \: p - 7 \sqrt{5}q }$

$\blue\Rsh \tt{ \frac{ 54 - 54 + 14 \sqrt{5} + 14 \sqrt{5} }{ 44 } = } \small \tt \blue{ \: p - 7 \sqrt{5}q }$

$\blue\Rsh \tt{ \frac{ \cancel{54 - 54} + 14 \sqrt{5} + 14 \sqrt{5} }{ 44 } = } \small \tt \blue{ \: p - 7 \sqrt{5}q }$

$\blue\Rsh \tt { \frac{28 \sqrt{5} }{ 44 } = } \small \tt \blue{ \: p - 7 \sqrt{5}q }$

$\blue\Rsh \tt { \frac{28 (\sqrt{5}) }{ 44 } = } \small \tt \blue{ \: p - 7 \sqrt{5}q }$

$\blue\Rsh \tt { \frac{ \cancel{28} (\sqrt{5}) }{ \cancel{ 44} } = } \small \tt \blue{ \: p - 7 \sqrt{5}q }$

$\blue\Rsh \tt { \frac{7 (\sqrt{5}) }{ 11} = } \small \tt \blue{ \: p - 7 \sqrt{5}q }$

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$\circledcirc \small\tt \blue{ \: Comparing \: values}$

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$\small \boxed{\tt {\underline{p = 0}}}$

$\small \boxed{\tt {\underline{q = \frac{1 }{11} }}}$

Answer 2

Answer:

Chlorophyll is any of several related green pigments found in the mesosomes of cyanobacteria and in the chloroplasts of algae and plants. Its name is derived from the Greek words χλωρός, khloros and φύλλον, phyllon. Chlorophyll is essential in photosynthesis, allowing plants to absorb energy from light.