if x=3-2root2, find the value of x²+1/x²
Answers
Answered by
1
Step-by-step explanation:
If x= 3+2√2, what is the value of x^2+1/x^2?
x=3+22–√1x=13+22–√=3−22–√9−8=3−22–√(x2+1x2)=(x+1x)2−2(x2+1x2)=(3+22–√+3−23–√)2−2(x2+1x2)=36−2=34
Given,
x=3+2√2
Inverse equatio,
1/x=1/3+2√2
=>1/x=(3–2√2){(3+2√2)(3–2√2)}
=>1/x=(3–2√2)/{(3)²-(2√2)²}
=>1/x=(3–2√2)/(9–8)
=>1/x=(3–2√2)/1
=>1/x=3–2√2
=>x+1/x=3+2√2+3–2√2
=>x+1/x=6
=>x²+1/x²=(x+1/x)² -2.x.1/x
=>x²+1/x² =(6)²-2
=>x²+1/x²=36–2
=>x²+1/x²=34
Ans.
Similar questions
Chemistry,
3 hours ago
English,
3 hours ago
Political Science,
5 hours ago
Math,
5 hours ago
Math,
7 months ago
Social Sciences,
7 months ago