Which of the following is an extraneous solution of (45-3x)^1/2 = x-9
x = -12, x = -3, x = 3, x = 12

Solution:

Given (45-3x)^½ = x-9

45-3x =( x-9 )² [Squaring on both sides]

45-3x = x² - 18x + 81

Bring this equation in the general form of the quadratic equation ax² + bx +c =0

x²-18x +3x +81 -45 =0

x²-15x +36=0

x= {-b±√(b² -4ac)} / 2a [Using the quadratic formula]

= {-(-15)±√((-15)² -4(1)(36))} / 2(1)

= {15±√(225 -144)} / 2

= (15±√81)/2

= (15 ± 9)/2

= 12,3

Thus the 2 solutions are 12,3

On verification, √(45-36) = 12 - 9

√9 =3

3 = 3

On verification, √(45-9) = 3-9

√36 = -6

6 ≠ -6

The extraneous solution is x = 3

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Which of the following is an extraneous solution of (45-3x)^1/2 = x-9
x = -12, x = -3, x = 3, x = 12

Summary:

The following are extraneous solutions of (45-3x)^1/2 = x-9, -12 and -3.