Question

if x=3-2root2, find the value of x²+1/x²​

Answer 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.