Does this:
sqrt 3x-4=(x-4)^2-3
Multiply out to:
x^4-16x^3+90x^2-111x+173
Once I know it is multiplied out right then I can continue. Thanks
i got 3x^2-16x+16
no
first of all, you don't have an equation as your answer.
√(3x-4)=(x-4)^2-3
square both sides
3x-4 = (x-4)^4 - 6(x-4)^2 + 9
3x - 4 = x^4 - 16x^3 + 96x^2 - 256x + 256 - 6x^2 + 48x - 96 + 9
x^4 - 16x^3 + 102x^2 - 211x + 166 = 0
Oh thanks didn't see this post.
I realized I needed to make it equal zero. I keep getting 90 x^2 instead of 102 and 173 instead of 166.
Why do they make this so hard?
the difficulty is that you have to square the whole side, not just each term.
I agree with you, that is a hard question at your level.
Solving the final equation would be a nightmare.
I'm looking at your solution and I can't figure out where that -6 came from.
To verify whether the equation, sqrt(3x-4) = (x-4)^2 - 3, multiplies out to x^4 - 16x^3 + 90x^2 - 111x + 173, we need to solve the equation and compare the two expressions.
Step 1: Square both sides of the equation to eliminate the square root:
(sqrt(3x-4))^2 = ((x-4)^2 - 3)^2
Simplifying the left side:
3x-4 = ((x-4)^2 - 3)^2
Step 2: Expand the square of (x-4)^2 - 3:
3x-4 = (x^2 - 8x + 16 - 3)^2
Simplifying the right side:
3x-4 = (x^2 - 8x + 13)^2
Step 3: Expand the square of (x^2 - 8x + 13)^2:
3x-4 = (x^4 - 16x^3 + 90x^2 - 104x + 169)
Now, we can see that the expanded form is x^4 - 16x^3 + 90x^2 - 104x + 169, which is different from x^4 - 16x^3 + 90x^2 - 111x + 173.
Therefore, the equation does not multiply out to x^4 - 16x^3 + 90x^2 - 111x + 173.