Question

if x+1/x=a then x³+1/x³​

Answer 1

Step-by-step explanation:

• If x+1/x=3, then what is the value of x³+1/x³=?
• As we see that the x has a power of 3 so we begin by cubbing the whole equation.

GIVEN x+1/x=a then x³+1/x³

_If

So :we start solving like:

x+1x=3

(x+1x)3=33

x3+3.x2.1x+3.x.1x2+1x3=27

(x3+1x3)+3.x2.1x+3.x.1x2=27

x3+1x3+(3x+3x)=27

x3+1x3+3(x+1x)=27

x3+1x3+3×3=27

x3+1x3+9=27

x3+1x3=18

Therefore the answer is 18

Answer 2

Answer:

$x^3 + \frac{1}{x^3} = a(a^2 - 3)$

Step-by-step explanation:

Given that, $x + \frac{1}{x} = a$  . . . . . . . . . . . .  (i)

$=> (x + \frac{1}{x})^3 = a^3$  [cubed both sides]

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

$=> x^3 + \frac{1}{x^3} + 3a = a^3$  [using equation (i)]

∴ $x^3 + \frac{1}{x^3} = a^3 - 3a = a(a^2 - 3)$