Question

if x^2 + 1/x^2 =23 evaluate x+ 1/x​

Answer 1

Answer: x + 1/x = 5

Explanation:

x² + (1/x²) = 23 --------(Given)

x² + (1/x)² = 23

we know, (a + b)² = a² + 2ab + b²

therefore, (x + (1/x))²

= x² + 2 (x)(1/x) + (1/x)²

=x² + 2 + (1/x²) =

=(x² + (1/x²)) + 2

put the value of x² + (1/x²) = 23

= 23 + 2 = 25

so, (x + (1/x))² = 25

x + 1/x = √25 , x + 1/x = 5

Hence the value of x + 1/x = 5

Additional identities to remember:

(a-b)² =a²-2ab+b²

(a+b)³=a³+3a²b+3ab²+b³

(a-b)³ =a³-3a²b+3ab²-b³

a²-b² = (a+b)(a-b)

a³-b³=(a-b) (a²+ab+b²)

a³+b³=(a+b)(a²-ab+b²)

Answer 2

Answer

x^2 + 1/x^2 = 23

=> x^2 + 1/x^2 + 2(x)(1/x) = 23 + 2(x)(1/x)

=> (x + 1/x)^2 = 25

=> x + 1/5 = 5, -5