Question

Study the steps shown to solve the given equation.

Answer 1

Answer:

The answer is -3 and 7. The extraneous solution is x = -3.

Step-by-step explanation:

Answer 2

Answer:

a) The possible solutions are:

x=7 and x=-3

b)The extraneous solution

is x=

Step-by-step explanation:

The last step gives us the possible solutions.

$(x + 3)(x - 7) = 0$

By the zero product property,

$x + 3 = 0 \: or \: x - 7 = 0$

This implies that:

$x = - 3 \: or \: x = 7$

The original equation is

$\sqrt{30 - 2x} = x - 3$

We substitute x=-3 to get;

$\sqrt{30 - 2 \times - 3} = - 3 - 3 \\ \sqrt{30 + 6} = - 6 \\ \sqrt{36} = - 6 \\ 6 = - 6$

This not true, therefore x=-3 is an extraneous solution.

We substitute x=7

$\sqrt{30 - 2 \times 7} = 7- 3 \\ \sqrt{30 - 14} = 4 \\ \sqrt{16} = 4 \\ 4 = 4$

Therefore x=7 is the only solution.