Question

If x^3 + 1/x^3 = 110 then find the value of x + 1/x... # RDSHARMA grade 9.​

Answer 1

Answer:

(x+1/x)^3 =x^3+1/x^3 +3(x+1/x)

=110+3(x+1/x)

x+1/x=a

a^3 - 3a-110=0

a=5 satisfies the above equation.

Therefore x+1/x=5

Answer 2

$\huge\bold\red{question : }$

$\bold\red{If \: x^3 + 1/x^3 = 110 \: then \: find \: the \: value \: of \: x + 1/x}$

$\huge\bold\green{solution : }$

$\underline\bold\blue{given : } \: \: \: \: \: \: \bold{ {x}^{3} + \frac{1}{ {x}^{3} } = 110}$

$\underline\bold\blue{to \: find : } \: \: \: \: \: \: \: \: \bold{x + \frac{1}{x} }$

$\underline\bold\blue{formula \: used : } \bold{(a + b {)}^{3} = { {a}^{} }^{2} + {b}^{2} 3ab(a + b)}$

$= > {x + {( \frac{1}{x}) }} \: = ({110})^{3} \\ = > {x}^{3} + \frac{1}{ {x}^{3 } }3x \times \frac{1}{x} (x + \frac{1}{x} ) = 1331000 \\ = > 110 + 3(x + \frac{1}{x} ) = 1331000 \\ = > 113 +(x + \frac{1}{x} ) = 1331000 \\ = > (x + \frac{1}{x} ) = 1331000 - 113 \\ = > \boxed{x + \frac{1}{x} = 132887}$