If x=5-root 21 /2 then find the value of x+1/x x^2+1/x^2
Answers
Answered by
203
Given ,
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
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
Answered by
49
Answer:x= 5-root 215-root 21
1/x = 2/5-root 21----1
so, 1/x= 2/5-root 21 multiply by 5+root 21/5+root 21 -----2
---1 + ----2
=5-root 21 /2 +10+2 root 21 /(5)sq - (root 21 )sq
=5-root 21/ 2 + 10+2 root 21 /25 -21
=5-root 21/2 + 10+2 root 21 /4
=10-2 root 21 +10 2 root 21
=20/4
=5
Step-by-step explanation:
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