Question

If x=9-4root5 then find the value of ( x^2+1/x^2​

Answer 1

Step-by-step explanation:

hope it help you

Answer 2

Answer:

x^{2} + 1/x^{2} =  322

Step-by-step explanation:

In the above mentioned question : x = 9-4√5 ........... equation 1.

now insert this equation 1. in x^{2} + 1/x^{2}. we get,

(9-4√5)² + 1/(9-4√5)²

= [(9-4√5)²(9-4√5)²+1] / (9-4√5)²

now we shall use the formula (a-b)²= a²+b²- 2ab to expand the numerator.

= [(9²+4²(√5)² - 2.9.4√5) (9²+4²(√5)² - 2.9.4√5) + 1 ] / (9²+4²(√5)² - 2.9.4√5)

= [ ( 81+80-72√5 )( 81+80-72√5 ) +1 ] /  ( 81+80-72√5 )

= [ ( 161-72√5 ) ( 161-72√5 ) + 1 ] / ( 161-72√5 )

= [ (161)² + (72)²(√5)² + 2.161.72√5 + 1 ] / ( 161-72√5 )

= [ 25921 + 25920 + 23184√5 + 1 ] / ( 161-72√5 )

= [ 51842 + 23184√5 ] / ( 161-72√5 )

= 322 ( 161-72√5 ) / ( 161-72√5 )

= 322