Solve each equation. Remember to check for extraneous solutions

Question

9) sqrt(3 − 2x )=sqrt( 1 − 3x) 10) sqrt(3k − 11 )=sqrt( 5 − k)

Answer 1

 9)

√(3 − 2x )  =  √( 1 − 3x) --------> (1)

Squaring on both sides

3 - 2x  =  1 - 3x

3x - 2x  =  1 - 3

x  =  - 2

Substitute x = - 2 in Eq (1)

√(3 − 2(-2) )  =  √( 1 − 3(-2))

√(3 + 4 )  =  √( 1 + 6))

√7  =  √7

Hence, No Extraneous Solutions

10)

√(3k − 11 )  =  √( 5 − k) ---------------------> (2)

Squaring on both sides

3k - 11  =  5 - k

3k + k  =  5 + 11

4k  =  16

k  =  16/4

k  =  4

Substitute k = 4 in Eq (2)

√(3(4) − 11 )  =  √( 5 − 4) 

√(12 − 11 )  =  √1

√1  =  √1

1  =  1

Hence, No Extraneous Solutions

Answer :

9) The solution is x = -2

10) The solution is k  =  4.