Question

if x=3+2√2,findx²+1/x²

Answer 1

Hey user here is your answer ☺️...

(a+b)²= a²+b²+2ab

= x²+1/x²+2

(3+2√2+1/3+2√2) ²-2

{3+2√2+(3-2√2)/3²-2√2²}-2

{3+2√2+(3-2√2)/9-8)²-2

{3+2√2+3-2√2}²-2

{6}²-2

36-2

34

simple and helpful

Answer 2

ʜᴇy ᴜꜱᴇʀ

ʜᴇʀᴇ ɪꜱ yᴏᴜʀ ᴀɴꜱᴡᴇʀ :-

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$x = 3 + 2 \sqrt{2} \\ \\ x + \frac{1}{x} = 3 + 2 \sqrt{2} + \frac{1}{3 + 2 \sqrt{2} } \\ \\ = 3 + 2 \sqrt{2} + \frac{3 - 2 \sqrt{2} }{(3 + 2 \sqrt{2} )(3 - 2 \sqrt{2}) } \\ \\ = 3 + 2 \sqrt{2} + \frac{3 - 2 \sqrt{2} }{ {3}^{2} - {(2 \sqrt{2} )}^{2} } \\ \\ = 3 + 2 \sqrt{2} + \frac{3 - 2 \sqrt{2} }{9 - 8} \\ \\ = 3 + 2 \sqrt{2} + 3 - 2 \sqrt{2} \\ \\ = 6 \\ \\ {(x + \frac{1}{x} )}^{2} = {x}^{2} + { \frac{1}{x} }^{2} + 2.x. \frac{1}{x} \\ \\ {6}^{2} = {x}^{2} + { \frac{1}{x} }^{2} + 2 \\ \\ {x}^{2} + { \frac{1}{x} }^{2} = 36 - 2 \\ \\ = 34$

ꜱᴏ ᴛʜᴇ ᴀɴꜱᴡᴇʀ ɪꜱ 34