Question

What are the steps in solving the problem: 8(m-4)^4-10(m-4)^2+3=0?

Answer 1

Use substitution \[ u=(m-4)^2 \] Then solve the quadrativ equation in u and substitute back.

Answer 2

*quadratic

Answer 3

You will find that the solutions are \[ \{ 4+1/2\,\sqrt {2},4-1/2\,\sqrt {2},4+1/2\,\sqrt {3},4-1/2\,\sqrt {3} \} \]

Answer 4

So you factor to u^2-( 5/4)u+(3/8)= 0 then use the quadratic formula?

Answer 5

Yes or complete the square.

Answer 6

That gives you the u values. Then you use the definition of u to find the m values. For each u value there will be 2 m values. So you get 4 solutions total, which makes sense as the original problem is of order 4.

Answer 7

Thank you.