Answers
Step-by-step explanation:
18
Step-by-step explanation:
Given:
x = \dfrac{ \sqrt{5} - 2 }{ \sqrt{5} + 2}x=
5
+2
5
−2
To Find:
x + \dfrac{1}{x}x+
x
1
Process to Solve:
1. Don't Need to Rationalize because it's a like fraction
2. Take L.C.M
3. Use Algebra Formula
4. Simplify and Get the answer
Simple, Isn't it ?
Solution:
\begin{gathered}x + \frac{1}{x} \\ \\ = \frac{ \sqrt{5} - 2}{ \sqrt{5} + 2} + \frac{ \sqrt{5} + 2}{ \sqrt{5} - 2} \\ \\ [\text{By taking L.C.M}] \\ \\ = \frac{ ( \sqrt{5} - 2) {}^{2} + {( \sqrt{5} + 2) }^{2} }{( \sqrt{5} + 2)( \sqrt{5} - 2) } \\ \\ = \frac{2 \{(\sqrt{5 }) {}^{2} + (2 {)}^{2} \} }{ {( \sqrt{5})}^{2} - {(2)}^{2} } \\ \\ = \frac{2(5 + 4)}{5 - 4} \\ \\ = \frac{2(9)}{1} \\ \\ = 18\end{gathered}
x+
x
1
=
5
+2
5
−2
+
5
−2
5
+2
[By taking L.C.M]
=
(
5
+2)(
5
−2)
(
5
−2)
2
+(
5
+2)
2
=
(
5
)
2
−(2)
2
2{(
5
)
2
+(2)
2
}
=
5−4
2(5+4)
=
1
2(9)
=18
Therefore, The required answer is 18.
Algebra Formula Used
a² - b² = (a + b)(a - b)
(a - b)² + (a + b)² = 2(a² + b²)
What is Like Fraction ?
When the nominator and denominator of two fraction are similar but different by sign.
Answer: