Question

if if x+1/x =6 then X3+1/x3 find the answer step by step ​

Answer 1

Given:-

•Value of (x+1/x)=6

To find:-

•Value of (x³+1/x³)

Solution:-

By cubing both the sides in the equation,(x+1/x)=6,we get:-

$= > (x + \frac{1}{x} ) ^{3} = (6) ^{3}$

We know that:-

=>(x+y)³=x³ + y³ + 3xy (x+y)

$= > {x}^{3} + \frac{1}{x ^{3} } + 3</strong><strong>×</strong><strong>x</strong><strong>×</strong><strong>1</strong><strong>/</strong><strong>x</strong><strong> (x + \frac{1}{x}) = 216$

$= > {x}^{3} + \frac{1}{x ^{3} } + 3(6) = 216$

$= > {x}^{3} + \frac{1}{x ^{3} } + 18 = 216$

$= > {x}^{3} + \frac{1}{x ^{3} } = 216 - 18$

$= > {x}^{3} + \frac{1}{x ^{3} } = 198$

Thus,value of x³+1/x³ is 198.

Some important identities:-

•(a+b)²= a² + b² + 2ab

•(a-b)²= a² + b² - 2ab

•a² - b² = (a-b)(a+b)

•(a+b+c)² = a² + b² + c² + 2(ab + bc +ca)

•(a+b)³ = a³ + b³ + 3ab(a + b)

•(a-b)³ = a³ - b³ - 3ab(a - b)

•a³ + b³ = (a + b)(a² + b² - ab)

•a³ - b³ = (a - b)(a² + b² + ab)