Question

if x=√3+2√2 , then what is the value of x²+1/x² ?​

Answer 1

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

Ans.

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Answer 2

Answer:

(286 + 96√6) / 25

Step-by-step explanation:

(√3+2√2)² + 1/(√3+2√2)²

= (11+4√6 ) + 1 /(11+4√6)

= (286+96√6)/25