Question

If x = 2 + 223 + 213 then find the value of x3-6x2+6x ?
A) 1
B) 2
C) 3
D) 4

Answer 1

Hey mate ^_^

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Answer:
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Given:

x$= 2 + {2}^{ \frac{2}{3} } + {2}^{ \frac{1}{3} }$

So,

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

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

By using,

$(a-b)^3= a^3 - b^3 - 3ab(a-b)$

And,

$(a+b)^3= a^3 + b^3 + 3ab(a+b)$

Now,

$x^3 - 8 - 6x^2 + 12x = 4 + 2 + 6(x-2)$

$x^3 - 8 -6x^2 + 12x = 6 + 6x - 12$

$x^3 - 6x^2 +6x = 2$

Therefore,

Correct option B) 2

#Be Brainly❤️

Answer 2

hey

here is answer

Given:

$x= 2 + {2}^{ \frac{2}{3} } + {2}^{ \frac{1}{3} }$

So,

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

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

By using, 

(a-b)^3= a^3 - b^3 - 3ab(a-b)

And, 

(a+b)^3= a^3 + b^3 + 3ab(a+b)

Now, 

x^3 - 8 - 6x^2 + 12x = 4 + 2 + 6(x-2)

x^3 - 8 -6x^2 + 12x = 6 + 6x - 12

x^3 - 6x^2 +6x = 2

hope it helps

thanks