Question

X+1/x=√5 find the value of x2+1/x2

Answer 1

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☞ x ²+ 1/x² = 3

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$\huge\sf\blue{Given}$

✭ $\sf x+\dfrac{1}{x}$

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$\huge\sf\gray{To \:Find}$

◈ $\sf x^2\dfrac{1}{x^2}$

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$\huge\sf\purple{Steps}$

$\bullet \: \underline{\textsf {Squaring both Sides}}$

$\dashrightarrow \sf{ \bigg \lgroup x + \frac{1}{x} \bigg \rgroup}^{2} = ( { \sqrt{5}) }^{2} \\ \\\dashrightarrow \sf {x}^{2} + { \frac{1}{x} }^{2} + 2 \lgroup\frac{1}{x} \rgroup x = 5 \\ \\\dashrightarrow \sf{x}^{2} + \frac{1}{ {x}^{2} } = 5 - 2 \\ \\ \orange{ \dashrightarrow\sf{x}^{2} + \frac{1}{ {x}^{2} } = 3}$

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Answer 2

Answer:

3

Step-by-step explanation:

(x +1/x)^2 = (√5)^2

x^2 + 1/x^2 +2 = 5

x^2 + 1/x^2 = 5 - 2 = 3