Question

If x=3+2√2 , find the value of x2 + (1/x2 ).​

Answer 1

Answer:

Here x=3+2√2 so

x^2=9+8+12√2

=17+12√2

Now 1/x^2 = (17-12√2)/(17^2-12√2^2)

= (17-12√2)/(289-288)

= 17-12√2

So x^2+1/x^2= 34

Answer 2

Step-by-step explanation:

Given,

x=3+2√2

Inverse equation,

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.