Question

plzz solve this urgent need

Answer 1

x = (5 - √21)/2

1/x = 2/(5 -√21)

=2(5 + √21)/(5 -√21)(5 + √21)

= (5 + √21)/2

hence,

x + 1/x = (5 -√21)/2 + (5+√21)/2 =5

Answer 2

Hello !!




Given that ; X = ( 5 - ✓21 / 2 )


Therefore,


1/X = 2/ ( 5 - ✓21 )





Rationalizing the denominator ( 5 - ✓21 )




1/X = ( 2 / 5 - ✓21 ) × ( 5 + ✓21 ) / ( 5 + ✓21 )





1/ X = 2 ( 5 + ✓21 ) / ( 5 - ✓21 ) ( 5 + ✓21 )




1/X = 2 ( 5 + ✓21 ) / ( 5)² - (✓21 )²



1/X = 2 ( 5 - ✓21 ) / 25 - 21




1/X = 2 ( 5 + ✓21 ) /4



1/X = ( 5 + ✓21 ) / 2



Therefore,



X + 1/X = ( 5 - ✓21 /2 + ( 5 + ✓21 /2 )



X + 1/X = ( 5 - ✓21 + ✓21 + 5 / 2 )




X + 1/X = 10/2 = 5.