Question

if x+x^-1 = 10 (x is not equal to 0) then find x^2+x^-2 with explanation

Answer 1

Answer:

98

Step-by-step explanation:

Since x+x^-1=10

So

(x+x^-1)²=(10)²

x²+x²^-1+2=100

x²+x²^-1=100-2

x²+x²^-1=98

Answer 2

Answer:

98

Step-by-step explanation:

Given:

x + x^-1 = 10

To find:

x² + x^-2

Solution:

$x + {x}^{ - 1} = 10 \\ \\ x + \frac{1}{x} = 10$

[Now , Squaring both side ]

${(x + \frac{1}{x} )}^{2} = {(10)}^{2} \\ \\ {x}^{2} + { \frac{1}{x {}^{2} } } + 2.x. \frac{1}{x} = 100 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 100 - 2 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 98 \\ \\ {x}^{2} + {x}^{ - 2} = 98$

Hence, the Required value is 98.

Using Formula,

(a + b)² = a²+ 2ab + b²