If x= 5 - root 21 /2, find the values of (j) x+1/x (ii) x^2+1/x^2
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31
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
x² + 1/x² = (x + 1/x)² -2x.1/x
= (x + 1/x)² -2
=(5)² -2
= 23
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
x² + 1/x² = (x + 1/x)² -2x.1/x
= (x + 1/x)² -2
=(5)² -2
= 23
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