Question

if x=3+2√2,find value of x^2+1/x^2(34)​

Answer 1

Step-by-step explanation:

there are two ways ...

1st way.

If x = 3 +2√2, then 1/x = 1/(3+2√2) =(3–2√2), because 3^2 -(2√2)^2 =9–8=1. Hence x^2 +(1/x^2) = [x+(1/x)]^2 -2 = 6^2 -2 =36 -2 = 34

2nd way.

• 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.

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