Question

Solve the equation after making an appropriate substitution, *4-6x² +8=0 Determine the appropriate substitution using the new variable u: U Write the new quadratic equation using the variable u: (Type an equation. Type your answer in standard form.) Solve the new quadratic equation for the variable u. u= (Simplify your answer. Type an integer or a simplified fraction. Use a comma to separate answers as needed.) The solution set to the original equation is a. (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)

Answer 1

Solution & - 6x² +8=0 Substitute u= So the new quadratic equation become. & 4²-64 +8=0 Now we solve it to find the valuesq u. write nou as a difference 4²-24-44 + 8 0 4(4-2) - 4 (4-2) 0 (4-2) (4-4) = 0 So, (4-2) =0 & (1-4)=0 Iso the values g u & 2, 4

Mow, we find the value of a we have the relation u = x So, when, u=2 x=+52 - 52 and when u=4 , 4=2? x=1 Tu x=2, -2 So, the solution set to the original equation is xi - 2, -se, de a