x^6-27=0 ?????

Question

x^6-27=0 ?????

anonymous · Answer

can some1 explain also

amistre64 · Answer

(x^2)^3 - 9^3 = 0

anonymous · Answer

difference of two cubes.  
$$a^3-b^3=(a-b)(a^2+ab+b^2)$$

anonymous · Answer

oh guru!

amistre64 · Answer

(x^2 - 9 ) (x^4 +9x^2 +81)

anonymous · Answer

in this case 
$$a=x^2$$ and 
$$b=3$$ then plug it in

amistre64 · Answer

lol ..... yeah 3^3 = 27 :)

anonymous · Answer

im so confused u serioiusly have to break it down 4 me lol

anonymous · Answer

i get 
$$(x^2-3)(x^4+3x^2+9)$$

amistre64 · Answer

there are certain times when you have to factor squares that are subtracted and cubes that are subtracted

anonymous · Answer

normally i would defer to my master but in this case it is not true that 
$$9^3=27$$

amistre64 · Answer

you need to have a good eye for it to spot them; and then recall the formula for the way the were created

amistre64 · Answer

i was using imaginary numbers lol

anonymous · Answer

yes and some creative exponents too!

amistre64 · Answer

gotta migrate to the veranda ;)

anonymous · Answer

with miranda?

anonymous · Answer

i'm warning you...

anonymous · Answer

@tiffanyjames i am sure my answer is correct.  i will explain if you like

anonymous · Answer

yes please but i thought the answer would b 2 numbers?

anonymous · Answer

no not two numbers

anonymous · Answer

you have the difference of two cubes

anonymous · Answer

we go slow

anonymous · Answer

$$x^6$$ is the cube of 
$$x^2$$ yes?

anonymous · Answer

the question said to find the 2 real solutions?

anonymous · Answer

ahh ok then we take only two steps.

anonymous · Answer

add 27 to both sides to get 
$$x^6=27$$

anonymous · Answer

gotcha

anonymous · Answer

then we write 
$$27=3^3$$ so we have 
$$x^6=3^3$$

anonymous · Answer

ok that was another step so i lied, we need 3 steps

anonymous · Answer

now take the sixth root to get x

anonymous · Answer

don't forget to write plus or minus

anonymous · Answer

we get 
$$x=\pm\sqrt[6]{3^3}$$

anonymous · Answer

how woudl i put that into a calculator?

anonymous · Answer

but you teacher will not except this answer because the sixth root of 3 cubed is the same as the square root of 3

anonymous · Answer

forget the calculator. just write 
$$x=\pm\sqrt{3}$$

anonymous · Answer

i hope it is clear that the sixth root of 3 cubed is the square root of 3

anonymous · Answer

yes

anonymous · Answer

you sure?

anonymous · Answer

fine i believe you.  you can just think of canceling the 3 in the exponent with the 6 in the 'radicand" to get 2 i.e. square root.  so those are your two real answers, 
$$\sqrt{3}$$ and 
$$-\sqrt{3}$$