Math, asked by BhawnaAggarwalBT, 1 year ago


plz solve it right now
it is urgent
if you can do my other questions also from my profile

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Answered by niya25
22
follow me.....................
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niya25: is it right
BhawnaAggarwalBT: wrong
Answered by abhi569
30
 \bold{a = \frac{ \sqrt{5} + 1 }{ \sqrt{5} - 1} }\\ \\ \bold{ \: by \: rationalization} \\ \\ \\ \\ \bold{a = \frac{ \sqrt{5} + 1}{ \sqrt{5} - 1} \times \frac{ \sqrt{5} + 1}{ \sqrt{5} + 1} \: \: \: \: \: \: \: \: \: \rightarrow \: a = \frac{5 + 1 + 2 \sqrt{5} }{5 - 1} \: \: \: \: \: \: \: \: \: \rightarrow \: a = \frac{6 + 2 \sqrt{5} }{4} \: \: \: \: \: \: \: \: \: \: \: \rightarrow \: a = \frac{3 + \sqrt{5} }{2} } \\ \\ \\ \bold{ \: {a}^{2} = {( \frac{3 + \sqrt{5}) }{2}) }^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \rightarrow \: {a}^{2} = \frac{9 + 5 + 6 \sqrt{5} }{4} \: \: \: \: \: \: \: \: \: \rightarrow \: {a}^{2} = \: \frac{14 + 6 \sqrt{5} }{4} \: \: \: \: \: \: \: \rightarrow \: {a}^{2} = \frac{7 + 3 \sqrt{5} }{2} }\: \: \: \: \: \: \: \: ...(i)

 \bold{ b = \frac{ \sqrt{5} - 1}{ \sqrt{5} + 1 } \: \: \: \: \: \: \: \: \:} \\ \\ \bold{ \: by \: rationalization} \\ \\ \\ \\ \bold{b = \frac{ \sqrt{5} - 1}{ \sqrt{5} + 1 } \times \frac{ \sqrt{5} - 1}{ \sqrt{5} - 1 } \: \: \: \: \: \: \: \: \: \: \: \rightarrow \: b = \frac{5 + 1 - 2 \sqrt{5} }{5 - 1} \: \: \: \: \: \: \: \: \: \: \: \rightarrow \:b = \frac{6 - 2 \sqrt{5} }{4} \: \: \: \: \: \: \: \: \: \: \: \rightarrow \: b = \frac{3 - \sqrt{5} }{2} } \\ \\ \\ \bold{ {b}^{2} = { (\frac{3 - \sqrt{5} }{2} )}^{2} \: \: \: \: \: \: \: \: \: \rightarrow \: {b}^{2} = \frac{9 + 5 - 6\sqrt{5} }{4} \: \: \: \: \: \: \: \: \: \: \: \rightarrow \: {b}^{2} = \frac{14 - 6 \sqrt{5} }{4} \: \: \: \: \: \: \: \: \: \: \: \: \: {b}^{2} = \frac{7 - 3 \sqrt{5} }{2} } \: \: \: \: \: \: \: ...(ii)



 \bold{ \: ab = \frac{ \sqrt{5} + 1}{ \sqrt{5} - 1 } \times \frac{ \sqrt{5} - 1}{ \sqrt{5} + 1} } \\ \\ \\ \bold{ab = 1} \: \: \: \: \: \: ....(iii)



 \bold{ \underline{ \: Now \: }}




 \bold{ \: \frac{ {a}^{2} + ab + {b}^{2} }{ {a}^{2} - ab + {b}^{2} }} \\ \\ \\ \\ \bold{ \: \: <br />Putting \: values \: from ( i ) , ( ii ) , ( iii ) , } \\ \\ \\ \bold{ \: = &gt; \: \: \frac{ \frac{7 + 3 \sqrt{5} }{2} + 1 + \frac{7 - 3 \sqrt{5} }{2} }{\frac{7 + 3 \sqrt{5} }{2} - 1 + \frac{7 - 3 \sqrt{5} }{2} } } \\ \\ \\ \\ = &gt; \bold{ \frac{ \frac{7 + 3 \sqrt{5} + 2 + 7 - 3 \sqrt{5}}{2} }{ \frac{7 + 3 \sqrt{5} - 2 + 7 - 3 \sqrt{5} }{2} } } \: \: \: \: \\ \\ \\ \\ = &gt; \bold{\frac{ \frac{16}{2} }{ \frac{12}{2} } } \\ \\ \\ \\ = &gt; \bold{ \: \frac{8}{6} } \\ \\ \\ \\ = &gt; \bold{ \: \frac{4}{3} }

Anonymous: Osm!!
abhi569: (-:
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