Question

if x+1/x=5 find the value of x²+1/x²​

Answer 1

Answer:

please find the answer in the attachment

Answer 2

♡ Answer:

$\: \boxed{ \sf {x}^{2} \: + \: \dfrac{1}{ {x}^{2} } \: = 23}$

♡ Solution:

We know that :

$\sf \: x \: + \: \dfrac{1}{x} \: = \: 5$

Now by squaring both sides, we get:

$\sf \: x \: + \: \dfrac{1}{x} \: = \: 5 \\ \implies \: \sf \: {( \: x \: + \: \dfrac{1}{x} \: )}^{2} \ = \: {5}^{2} \\ [ \because \: { {( \sf \: a \: + \: b)}^{2} \: = \: \sf {a}^{2} \: + \: 2ab \: + \: {b}^{2} ) }^{2} ] \\ \sf \: \implies \: {x}^{2} \: + \: \dfrac{1}{ {x}^{2} } \: + \: 2 \: = \: 25 \\ [ \: \sf \because \: 2 \: \times \: x \: \times \: \frac{1}{x} \: = \: 2] \: \\ \sf \: \implies \: {x}^{2} \: + \: \dfrac{1}{ {x}^{2} } \: = \: 25 \: - \: 2 \\ \sf \: \implies \: \boxed{ \sf {x}^{2} \: + \: \dfrac{1}{ {x}^{2} } \: = 23}$

♡ Extra - Information:

• a² – b² = (a – b)(a + b)

• (a + b)² = a² + 2ab + b²

• a² + b² = (a + b)² – 2ab

• (a – b)² = a² – 2ab + b²

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

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

• (a + b)³ = a³ + 3a²b + 3ab² + b³

• (a + b)³ = a³ + b³ + 3ab(a + b)

• (a – b)³ = a³ – 3a²b + 3ab² – b³ = a³ – b³ – 3ab(a – b)

• a³ – b³ = (a – b)(a² + ab + b²)