Question

If x = 3 + 2√2 , find :
(a) x +1/x
(b) x² + 1/x​

Answer 1

Answer:

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

If x=3-2√2, then what is the value of (√x) - (1/√x)?

If x=3+2√3, then what is the value of √x+1/√x?

If x= 3+2√2, then what is the value of (x+1/x)?

If x=3+2√2, then what is the value of √x-1/√x?

What is the value of (x2+1/x2)(x4+1/x4)/(x3+1/x3) , when x+1/x=3-2√2?

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.