Solving Fancy Quadratics (2.6.3)

Question 1

• Frequently, an equation that appears to be of higher degree than a squared term can be rewritten so that your quadratic techniques allow you to solve it

Answer 1

• Frequently, an equation that appears to be of higher degree than a squared term can be rewritten so that your quadratic techniques allow you to solve it

Question 2

• Be creative with your use of variables. Look for ways to use them so that you can see your equation as a quadratic and use all your tools.

Answer 2

• Be creative with your use of variables. Look for ways to use them so that you can see your equation as a quadratic and use all your tools.

Question 3

• Remember that whenever you solve an equation by substituting in a new variable, you must replace that variable when you have found its solution. At that point, you reinsert the original variable and solve for its values from this much simplified equation.

Answer 3

• Remember that whenever you solve an equation by substituting in a new variable, you must replace that variable when you have found its solution. At that point, you reinsert the original variable and solve for its values from this much simplified equation.

Question 4

Since you have x^2 and its square x^4 in this equation, substitute in a new variable that equals x^2.

Now solve the equation as a quadratic.

Substitute x^2 back in for the variable.

Solve for x. Expect four answers because your variable was originally raised to the fourth degree.

Answer 4

Since you have x^2 and its square x^4 in this equation, substitute in a new variable that equals x^2.

Now solve the equation as a quadratic.

Substitute x^2 back in for the variable.

Solve for x. Expect four answers because your variable was originally raised to the fourth degree.

Question 5

This example works much the same way.

Since you have x^3 and its square x^6, you can substitute in a new variable for x^3.

Then solve the equation with the new variable.

Finally, substitute x^3 for the new variable and solve for x.

Answer 5

This example works much the same way.

Since you have x^3 and its square x^6, you can substitute in a new variable for x^3.

Then solve the equation with the new variable.

Finally, substitute x^3 for the new variable and solve for x.