Question

if x+1/x=3 evaluate
i.x-1/x
ii.x²+1/x²
iii.x⁴+1/x⁴

the answers are i.+5 ii.7 and iii.47


solve with the process ​

Answer 1

$x + \frac{1}{x} = 3 \\ squaring \: both \: sides \\ ( {x + \frac{1}{x} })^{2} = 9...(1) \\ \implies \: ( {x - \frac{1}{x} })^{2} + 4 = 9 \\ \implies \: ( {x - \frac{1}{x} })^{2} = 5 \\ x - \frac{1}{x} = \sqrt{5} \\ \\ from \: eqn \: (1) \: \: \: ( {x + \frac{1}{x} })^{2} = 9 \\ \implies {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 9 \\ \implies{x}^{2} + \frac{1}{ {x}^{2} } = 7 \\ again \: squaring \: both \: sides \\ ( { {x}^{2} + \frac{1}{ {x}^{2} } })^{2} = 49 \\ \implies {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 49 \\ \implies {x}^{4} + \frac{1}{ {x}^{4} } = 47$

Answer 2

ʜᴇy ᴋʀɪꜱʜ ᴩʟᴇᴀꜱᴇ ʀᴇꜰᴇʀ ᴛᴏ ᴀᴛᴛᴀᴄʜᴍᴇɴᴛ