Tomorrow is my final

[Guest]

Hi guys (and girls)

Could you PLEASE explain to me how the following problems are suppose to be done? I have looked and looked in my book and I do not see anything that remotely covers this.

Find all real solutions to the following equation;

8x^6+63x^3-8=0

4a-5sqrt(a)+1=0

 

[stapel]

They're expecting you to notice quadratic forms. No, these aren't quadratics, but they are of a similar form, so quadratic techniques might apply.

A quadratic form looks like:

. . . . .a[Y]² + b[Y] + c

...where "[Y]" is something other than just "x". In your case:

. . . . .8[x³]² + 63[x³] - 8 = 0

. . . . .4[sqrt(a)]² - 5[sqrt(a)] + 1 = 0

Can you see how to work these now?

Eliz.

 

[samantha ryan]

I think this might help!

1.8x^6+63x^3-8=0

x^3(8x^2+63x-8)=0
x^3(8x^2+64x-1x-8)=0
x^3[8x(x+8)-1(x+8)]=0
x^3(8x-1)(x+8)=0
x^3=0 (x+8) (8x-1)
x=0 x+8=0 8x-1=0
-8 -8 -1 -1
x=-8 8x=-1, divide both sides by 8
x=-1/8
x=-8
x=-1/8
x=0



2. 4a-5a^2+1=0


multiply everything by the negative -(-5a^2+4a+1)=0
5a^2-4a-1=0
5a^2-5a+1a-1=0
5a(a-1)+1(a-1)=0
(5a+1)(a-1)=0
5a+1=0 a-1=0
-1 -1 +1 +1
5a=-1 a=1
divide by 5


a=-1/5
a=1

 

[Denis]

I think this might help!
1.8x^6+63x^3-8=0
x^3(8x^2+63x-8)=0
x^3(8x^2+64x-1x-8)=0
x^3[8x(x+8)-1(x+8)]=0
x^3(8x-1)(x+8)=0
x^3=0 (x+8) (8x-1)
x=0 x+8=0 8x-1=0
-8 -8 -1 -1
x=-8 8x=-1, divide both sides by 8
x=-1/8
x=-8
x=-1/8
x=0

How in heck do you explain that, Samantha?
x^3(8x^2+63x-8) = 8x^5 + 63x^4 - 8x^3 ;
that's a far cry from 8x^6 + 63x^3 - 8 :!:

And your 3 solutions do not check out; take x = 0:
8x^6 + 63x^3 - 8 = 0
0 + 0 - 8 = 0 ??
Same thing with your other 2 solutions.

I get x=1/8 or x=-2 (which checks out) this way:

8x^6 + 63x^3 - 8 = 0 ; let a = x^3, then:
8a^2 + 63a - 8 = 0
(8a - 1)(a + 8) = 0
a = 1/8 or a = -8

x^3 = 1/8 or x^3 = -8
x = 1/2 or x = -2

 

[stapel]

I think this might help!

How?

Eliz.