12.3 Solving Radical Equations Algebra 12.3 Solving Radical Equations

Solve 1) √x – 7 = 1 2) √x – 10 = -3 +7 +7 +10 +10 √x = 8 ( )2 ( )2 Let’s Try!! You Try!! 1) √x – 7 = 1 2) √x – 10 = -3 +7 +7 +10 +10 √x = 8 ( )2 ( )2 √x = 7 ( )2 ( )2 x = 64 x = 49 Check it!! Check it!!

Isolate the Radical then Solve Let’s Try!! You Try!! 3) √2x – 3 + 3 = 8 4) √3x + 1 – 2 = 6 -3 -3 +2 +2 √2x – 3 = 5 ( )2 ( )2 √3x + 1 = 8 ( )2 ( )2 2x – 3 = 25 3x + 1 = 64 +3 +3 -1 -1 2x = 28 3x = 63 x = 14 x = 21 Check it!! Check it!!

Checking for Extraneous Solutions Let’s Try!! You Try!! 5) √x + 2 = x ( )2 ( )2 6) √x + 13 = 2 -13 -13 x + 2 = x2 -x – 2 -x – 2 √x = -11 ( )2 ( )2 0 = x2 – x – 2 x = 121 0 = (x – 2)(x + 1) Check it!! x = 2, -1 Check them!! 121 does not check! x = 2 -1 does not check! No solution!

Geometric Mean ( )2 ( )2 ( )2 ( )2 The geometric mean of a and b is √ab . Let’s Try!! You Try!! 7) The geometric mean of m and 6 is 12. Find the value of m. 8) The geometric mean of x and 4 is 10. Find the value of x. Geometric Mean = √6m Geometric Mean = √4x ( )2 ( )2 ( )2 ( )2 12 = √6m 10 = √4x 144 = 6m 100 = 4x 6 6 4 4 24 = m 25 = x

Try one from the HW Together P. 725 #35

HW P. 725 #15-53 Odd