if x= 3+2root 2
find the value of x²+1/x²
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Answer:
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
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