Question

if X+1/X=7 then find x³+1/x³​

Answer 1

Answer:

Firstly we will find x using

$\large{ \frac{x + 1}{x} = 7 }$

As

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \large{ \frac{x + 1}{x} = 7 } \\ \\ \implies x + 1 = 7x \\ \\ \implies \boxed{ x = \frac{1}{6} }$

Now We can find reqrd value as:)

${x}^{3} + \large\frac{1}{ {x}^{3} } \\ \\ =216 + \frac{1}{216} \\ \\ = \frac{46656 + 1}{216} \\ \\ = \frac{ 46657}{216}$

WHICH IS REQUIRED ANSWER

Answer 2

$\huge\fbox\green{\fbox\green{Solution:-}}$

$\huge\fbox\green{\fbox\blue{Given:-}}$

$x + \frac{1}{x} = 7$

$\huge\fbox\green{\fbox\purple{To \: Find:-}}$

${x}^{3} + {\frac{1}{x} }^{3} = ?$

$\huge\fbox\green{\fbox\pink{By \: the \: problem}}$

$(x + \frac{1}{x} ) = 7 \\ = > {(x + \frac{1}{x} )}^{3} = {7}^{3} - - - - (cubing \: both \: sides)\\ = > {x}^{3} + \frac{1}{ {x}^{3} } + 3 \times x \times \frac{1}{x} (x + \frac{1}{x} ) = 343 \\ = > {x}^{3} + \frac{1}{ {x}^{3} } + 3 \times 7 = 343 - - - - (x + \frac{1}{x} ) = 7 \\ = > {x}^{3} + \frac{1}{ {x}^{3} } = 343 - 21 \\ = 322(ans)$

$\huge\fbox\blue{\fbox\pink{formula \: used \: here}}$

$\huge\fbox\green{\fbox\blue{Answer = 322}}$

${(x + \frac{1}{x} )}^{3} \\ = {x}^{3} + \frac{1}{({x})^3} + 3 \times x \times \frac{1}{x} \times (x + \frac{1}{x)}$

$\fbox\green{\fbox\orange{Done \: by \: Aritra \: kar}}$