Question

if x+1/x=5/2, find the value of x³+1/x³​

Answer 1

Answer:

65/8

Step-by-step explanation:

Given :

(x + 1/x) = 5/2

Cubing on both sides, we get

⇒ (x + 1/x)³ = (5/2)³   ---- (1)

We know the algebraic identity,

( a + b )³  = a³ + b³ + 3ab ( a + b )

Or

a³ + b³ = ( a + b )³ - 3ab( a + b )

So,

Equation (1) becomes,

x³ + 1/x³ = (x + 1/x)³ - 3 * x * 1/x * (x + 1/x)

⇒ (x + 1/x)³ - 3(x + 1/x)

⇒ (5/2)³ - 3(5/2)

⇒ (125/8) - (15/2)

⇒ 65/8

Hope it helps!

Answer 2

$\tt \green{given : }$

$\tt \green{ \dag \: \frac{x + 1}{x} = \frac{5}{2} }$

$\tt \red{too \: find : }$

$\tt \red{ \dag \: \frac{ {x}^{3} + 1 }{ {x}^{3} } }$

$\tt \blue{answer : }$

$\tt \blue{2(x + 1) = 5x}$

$\tt \blue{2x + 2 = 5x}$

$\tt \blue{2 = 5x - 2x}$

$\tt \blue{2 = 3x}$

$\tt \blue{x = \frac{2}{3} }$

Fill the x value in the above equation.

you will get the answer.