Math, asked by Sanjeetyadavmzp, 1 year ago

If
X+1/x=4


Then,

X^4+1/x^4=?

Attachments:

sni2200O: x+1/x=4,or x+1=4x,or 3x=1 or x=1/3. and then x^4+1/x^4=(1/3^4+1)/1/3^4=82

Answers

Answered by sni2200O
16
x+1/x=4
or,x+1=4x
or,3x=1
or,x=1/3

and the answer is...
x^4+1/x^4=(1/3^4+1)/1/3^4=82

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Answered by MsQueen
23
Hey mate !


• Given :

x + 1/x = 4

• To find ;

x⁴ + 1 / x⁴

• Solution :

 \mathsf{x +  \frac{1}{x}  = 4} \\  \\  \mathsf{on \: squaring \: both \: sides..} \\  \\  \mathsf{(x +  \frac{1}{x}) {}^{2} = (4) {}^{2} } \\  \\  \mathsf{x {}^{2}  +  \frac{1}{x {}^{2}  } + 2 = 16 } \\  \\  \mathsf{x {}^{2}  +  \frac{1}{x {}^{2} } = 16 - 2 } \\  \\  \mathsf{x {}^{2}  +  \frac{1}{x {}^{2} } =14} \\  \\  \mathsf{on \: squaring \: both \: sides..} \\  \\\mathsf{ (x {}^{2}   +  \frac{1}{x {}^{2} } ) {}^{2}  = (14) {}^{2}} \\  \\\mathsf{x {}^{4}  +  \frac{1}{x {}^{4} }  + 2} = 196 \\  \\ \mathsf{x {}^{4}  +  \frac{1}{x {}^{4} } = 196 - 2} \\  \\  \boxed{ \bold{x {}^{4}  +  \frac{1}{x {}^{4} } = 194}}


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Thanks for the question !

Sanjeetyadavmzp: Shukriya dost
sni2200O: welcome dear
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