Question

Please, help
Pic inside

Answer 1

First rearrange:
\[4^{3x^2 -x}-2*8^{x^2 +\frac{ x }{ 3 }}<8\]

Answer 2

Now what can you notice here?
What is common with these numbers: 4,2,8,8?

Answer 3

4 is 2^2, 8 is 2^3

Answer 4

Yes! So try to rewrite the above equation using only the powers of 2

Answer 5

\[( 2^{3x ^{2}-x})^{2} - 2*(2^{x ^{2}+\frac{ x }{ 3 }})^{3} <2^{3}\]

Answer 6

what now? @Andras

Answer 7

You can expand the brackets. But after that I am bit stuck, thinking

Answer 8

I think there must be another way, when we can replace something and then solve

Answer 9

Oh yeah.... I wrote it down wrong

Answer 10

One minus error makes it harder

Answer 11

On the RHS there is \[8^{x^2+\frac{ x }{ 3 }} = 2^{3x^2+x}\]

Answer 12

Lets say \[a = 2^{3x^2+x}\]

Answer 13

Now on the RHS there is \[4^{3x^2+x}=a^2\]

Answer 14

This we have
\[a^2-2a-8<0\]

Answer 15

\[a _{1}=4\]
\[a _{2}=-2\]

Answer 16

Has to be in between -2 and 4 to be below 0
Now solve for x and done.

Answer 17

Now i understand, thank you!