Question

Two possible solutions of √11-2x=√x^2+4x+4 are –7 and 1. Which statement is true? A) Only x = –7 is an extraneous solution.
B) Only x = 1 is an extraneous solution.
C) Both solutions are extraneous.
D)Neither solution is extraneous.

Answer 1

Answer:

Option D)Neither solution is extraneous.

Step-by-step explanation:

we have

$\sqrt{11-2x}=\sqrt{x^{2}+4x+4}$

we know that

two possible solutions are x=-7 and x=1

Verify each solution

Substitute each value of x in the expression above and interpret the results

1) For x=-7

$\sqrt{11-2(-7)}=\sqrt{-7^{2}+4(-7)+4}$

$\sqrt{25}=\sqrt{25}$

$5=5$ ----> is true

therefore

x=-7 is not a an extraneous solution

2) For x=1

$\sqrt{11-2(1)}=\sqrt{1^{2}+4(1)+4}$

$\sqrt{9}=\sqrt{9}$

$3=3$ ----> is true

therefore

x=1 is not a an extraneous solution

therefore

Neither solution is extraneous

Answer 2

Answer:D

Step-by-step explanation: