Question

X+1/x=root 5 find value of x2 + 1/x2

Answer 1

Step-by-step explanation:

Given:

X+1/x=root 5

To find:

x2 + 1/x2

$x + \frac{1}{x} = \sqrt{5}$

Square Both sides

${(x + \frac{1}{x} )}^{2} = ( { \sqrt{5}) }^{2} \\ \\ {x}^{2} + { \frac{1}{x} }^{2} + 2( \frac{1}{x} )x = 5 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 5 - 2 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 3$

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•(a + b)² = a² + b² + 2ab

More you should know:-

•(a -b)² = a² + b² - 2ab

•(a + b)³ = a³ + b³ + 3ab(a+b)

•(a - b)³ = a³ + b³ - 3ab(a-b)

•(a + b)(a-b)= a² - b²

•(a + b)² = a² + b² + 2ab

• a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)

•(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.

•(x⁴ – 1) = (x² + 1)((x)² –(1)²) = (x² + 1)(x + 1)(x – 1)