Question

Check for extraneous solutions.
1.\[\sqrt{x-3}=x-3\]

2.\[\sqrt{5x-9}=x-9\]

Answer 1

please show the work

Answer 2

square both sides. you will get a quadratic equation and then solve the quadratic

Answer 3

\[\sqrt{x-3}=x-3 \rightarrow x-3 = (x-3)^{2}\rightarrow x-3 = x ^{2}-6x+9\]

Answer 4

x=3

Answer 5

\[x ^{2}-7x+12 =0 \rightarrow x=3,4\]

Answer 6

x^2-7x+12=0
\[(x-3)(x-4)=0\]

Answer 7

the second problem is the same as the first problem, with different numbers. follow the same procedure

Answer 8

5x-9=x^2-18x+81
x^2-23x+90=0
(x-18)(x-5)=0
x=18,5