Question

15) If x+1/x =4
1)x⁴+1/x⁴​

Answer 1

Answer:

1)x⁴+1/x⁴ = 194

Step-by-step explanation:

$\tt \bold \red{༒︎To Fɪɴᴅ:-}$

• Value of x⁴+1/x⁴

$\tt \bold \red{༒︎ Given:-}$

• x+1/x =4

$\tt \bold \red{༒︎ Formula:-}$

$\tt ({x + \frac{1}{x} )}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x}$

✯Nᴏᴡ ᴘᴜᴛ ᴛʜᴇ ᴠᴀʟᴜᴇ ɪɴ ғᴏʀᴍᴜʟᴀ

$\tt \to {4}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ \tt \to16 = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ \tt \to{x}^{2} + \frac{1}{ {x}^{2} } = 16 - 2 \\ \tt \to{x}^{2} + \frac{1}{ {x}^{2} } = 14$

✯Nᴏᴡ ᴀɢᴀɪɴ ʀᴇᴘᴇᴀᴛ ᴛʜᴇ ᴘʀᴏᴄᴇss ᴛᴏ ғɪɴᴅ Value of x⁴+1/x⁴

$\tt \bold \red{༒︎ Formula:-}$

$\tt ({ {x}^{2} + \frac{1}{ {x}^{2} } )}^{2} = { ({x}^{2} )}^{2} + \frac{1}{ { ({x}^{2} )}^{2} } + 2 \times {x}^{2} \times \frac{1}{ {x}^{2} }$

✯Nᴏᴡ ᴘᴜᴛ ᴛʜᴇ ᴠᴀʟᴜᴇ ɪɴ ғᴏʀᴍᴜʟᴀ

$\tt \to {14}^{2} = {x}^{4} + \frac{1}{ {x}^{4} } + 2 \\ \tt \to196 = {x}^{4} + \frac{1}{ {x}^{4} } + 2 \\ \tt \to {x}^{4} + \frac{1}{ {x}^{4} } = 196 - 2 \\ \tt \to {x}^{4} + \frac{1}{ {x}^{4} } = 194$

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❀Tʜᴀɴᴋs ғᴏʀ ǫᴜᴇsᴛɪᴏɴ❀

Answer 2

Answer:

therefore the answer is "194"