Question

if x²+¹/x²=7. find the value of x³+¹/x³​

Answer 1

Answer:

±18

Step-by-step explanation:

$x^{3} +\frac{1}{x^{3} } \\\\ = ( x +\frac{1}{x} )(x^{2} -x.\frac{1}{x} +\frac{1}{x^{2} } )\\\\= ( x +\frac{1}{x} )(7 -1 )$since  $(x^{2} +\frac{1}{x^{2} }) =7$

$=6(x +\frac{1}{x} )$

now,

$(x^{2} +\frac{1}{x^{2} }) =7$

⇒ $(x +\frac{1}{x})^{2} - 2x.\frac{1}{x} =7$

⇒$(x +\frac{1}{x})^{2} - 2 =7$

⇒$(x +\frac{1}{x})^{2} =9$

⇒ $(x +\frac{1}{x})=$±3

Hence, final answer is

$x^{3} +\frac{1}{x^{3} } =$ ± 18