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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

**Solution:**

Given (45-3x)^{½} = x-9

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

45-3x = x^{2} - 18x + 81

Bring this equation in the general form of the quadratic equation ax^{2} + bx +c =0

x^{2}-18x +3x +81 -45 =0

x^{2}-15x +36=0

x= {-b±√(b^{2} -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

## 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.

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