Equations Reducible to Quadratic Section 11.5 Equations Reducible to Quadratic

Recall Power to Power Rule (ab)c = abc Example : Use the power to power rule. X6 = (x3)2 X4 y10 This rule will be used to create the power of 2. With the power of 2 we can use the quadratic formula to solve the equation.

Creating the power of 2 Put the equation in decreasing order Look at the variable and power of the middle term That term squared should be the variable and power of the leading term. The middle variable and power will be your let statement. Let us practice

Practice Find the let statement x4 – 9x2 + 8 = 0 Rearrange ? No need x4 – 9x2 + 8 Middle term x2 First term x4 = (x2)2 Let y = x2 New equation y2 -9y + 8 Find the let statement t4 + 4 + 5t2 = 0 Rearrange? Middle Term First Term Let New equation

More Difficult Practice Find the let statement (x² + 7)²– 6(x² + 7)² – 16 = 0 Rearrange ? Middle term First term Let New equation Find the let statement -2√r + r – 6 = 0 Rearrange? Middle Term First Term

How to Solve with this method Create the equal zero Write the equation in decreasing order Compare the middle and first term to see if you can make the comparison Make the let statement Rewrite the equation with the new variable Solve the new equation Substitute the old term in for the new one Solve for the correct variable Check

Example Solve x4 – 9x2 + 8 = 0 Let y = x² y² – 9y + 8 = 0 y = 1 OR y = 8 1 = x² OR 8 = x² -1 = x or 1 = x OR 2√2 = x or -2√2 = x All answers check out

Example Solve t4 + 4 + 5t2 = 0

Example Solve (x² + 7)²– 6(x² + 7)² – 16 = 0

Example Solve -2√r + r – 6 = 0

Homework Section 11.5 #5-10, 13, 17, 23, 25, 31