if x=6+√7,then find the value of x²+1/x²
Answers
x=6+√7
x²+1/x²= (6+√7)²/1/(6+√7)²
36+7 / 1 / 36+7
(36+7)-(36+7)/1
=0
3278+24√7
3278+24√7 43-12√7
Step-by-step explanation:
x=6+√7
1/x=1/(6+√7)
=1(6-√7)/(6+√7)(6-√7)
=[6-√7]/[(6)²-(√7)²]
=(6-√7)/36-7
=(6-√7)/29
We know that,
(x+1/x)²=x²+1/x²+2
x²+1/x²=(x+1/x)²-2
={(6+√7+1/(6-√7)/29}²-2
={(6+√7)+29/ (6-√7)}²-2
= {[(6+√7)(6-√7)+29]/ (6-√7)}²-2
=(36-7+29)² -2
( 6-√7)²
= 58². -2
36+7-12√7
= 3364. -2
43-12√7
= 3364-2(43-12√7)
43-12√7
=3364-86+24√7
43-12√7
=3278+24√7
43-12√7
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