Question

If x+1/x=7 , then find the value of x³+1/x³​

Answer 1

Answer:

Step-by-step explanation:

(x+1/x)³=343

x³+1/x³+3(x+1/x)(x×1/x)=343

x³+1/x³+3(x+1/x)=343

Given x+1/x=7.

So x³+1/x³+(3×7)=343

So x³+1/x³+21=343

x³+1/x³​=322

Answer 2

Answer:

322

Step-by-step explanation:

Given that ;

$\sf x + \dfrac{1}{x} = 7$

On cubing both sides ;

$\sf \left(x + \frac{1}{x} \right)^3 = (7) {}^{3} \\ \\ \sf {x}^{3} + \frac{1}{ {x}^{3} } + 3 \: . \:x \:. \: \frac{1}{x} (x + \frac{1}{x} ) = 343 \\ \\ \sf {x}^{3} + \frac{1}{ {x}^{3} } + 3(x + \frac{1}{x} ) = 343 \\ \\ \sf {x}^{3} + \frac{1}{ {x}^{3} } + 3(7) = 343 \\ \\ \sf {x}^{3} + \frac{1}{ {x}^{3} } + 21 = 343 \\ \\ \sf {x}^{3} + \frac{1}{ {x}^{3} } = 343 - 21 \\ \\ \boxed{ \red{ \bf \therefore \: {x}^{3} + \frac{1}{ {x}^{3} } = 322}}$