Question

If x = 5 - 2 under root 6 then find the value of x square + 1/x square

Answer 1

Answer:

x² + 1/x² = 98

Step-by-step explanation:

x = 5 - 2√6

x² + 1/x²

= (x + 1/x)² - 2

={ (5 - 2√6)   +  1/(5 -2√6)}² -2

= { (5 - 2√6)   + (5+2√6)/(25 -24)}² - 2

= { (5 - 2√6)   + (5+2√6)/1}² - 2

= { (5 - 2√6)   + (5+2√6)}² - 2

= 10² - 2

= 100 -2

= 98

or

x² + 1/x²

= (x - 1/x)² + 2

={ (5 - 2√6)   -  1/(5 -2√6)}² + 2

= { (5 - 2√6)   - (5+2√6)/(25 -24)}² + 2

= { (5 - 2√6)  - (5+2√6)/1}² + 2

= { (5 - 2√6)  - (5+2√6)}² + 2

= (-4√6)}² + 2

= 16*6 + 2

= 96 + 2

= 98

Answer 2

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