if x = 9 − 4√5 find the value of x 2 − 1 x 2 and √x + 1 √x
Answers
Answer:
\begin{gathered}x = 9 - 4 \sqrt{5} \\ \\ \frac{1}{x} = \frac{1}{9 - 4 \sqrt{5} } \\ \\ \frac{1}{x} = \frac{1}{9 - 4 \sqrt{5} } \times \frac{9 + 4 \sqrt{5} }{9 + 4 \sqrt{5} } \\ \\ \frac{1}{x} = \frac{9 + 4 \sqrt{5} }{ {(9)}^{2} - {(4 \sqrt{5} )}^{2} } \\ \\ \frac{1}{x} = \frac{9 + 4 \sqrt{5} }{81 - 80} \\ \\ \frac{1}{x} = 9 + 4 \sqrt{5} \end{gathered}
x=9−4
5
x
1
=
9−4
5
1
x
1
=
9−4
5
1
×
9+4
5
9+4
5
x
1
=
(9)
2
−(4
5
)
2
9+4
5
x
1
=
81−80
9+4
5
x
1
=9+4
5
Now,
\begin{gathered} {x}^{2} + \frac{1}{ { x}^{2} } = {(9 - 4 \sqrt{5}) }^{2} + {(9 + 4 \sqrt{5} )}^{2} \\ \\ = 81 + 80 - 72 \sqrt{5} + 81 + 80 + 72 \sqrt{5} \\ \\ = 81 + 80 + 81 + 80 \\ \\ = 161 + 161 \\ \\ = 322\end{gathered}
x
2
+
x
2
1
=(9−4
5
)
2
+(9+4
5
)
2
=81+80−72
5
+81+80+72
5
=81+80+81+80
=161+161
=322
Step-by-step explanation:
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Answer:
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°°° ANSWER ➡ volve is 322 °°°
