DeathFightervx
contestada

Study the steps shown to solve the given equation.
(√30 - 2x)= x - 3
30 - 2x = x2 - 6x + 9
0 = x2 - 4x - 21
0 = (x + 3)(x - 7)
Based on the above work, possible solutions of the equation are
and
Check the answers in the original equation. The extraneous solution
is x=

Respuesta :

kudzordzifrancis

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.

[tex](x + 3)(x - 7) = 0[/tex]

By the zero product property,

[tex]x + 3 = 0 \: or \: x - 7 = 0[/tex]

This implies that:

[tex]x = - 3 \: or \: x = 7[/tex]

The original equation is

[tex] \sqrt{30 - 2x} = x - 3[/tex]

We substitute x=-3 to get;

[tex]\sqrt{30 - 2 \times - 3} = - 3 - 3 \\ \sqrt{30 + 6} = - 6 \\ \sqrt{36} = - 6 \\ 6 = - 6 [/tex]

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

We substitute x=7

[tex]\sqrt{30 - 2 \times 7} = 7- 3 \\ \sqrt{30 - 14} = 4 \\ \sqrt{16} = 4 \\ 4 = 4[/tex]

Therefore x=7 is the only solution.

MrRoyal

The possible solutions are -3 and 7, and the extraneous solution is x = -3,

From the steps shown, the last step is:

[tex]0 = (x + 3)(x - 7)[/tex]

Rewrite as:

[tex](x + 3)(x - 7)=0[/tex]

Split

[tex](x + 3)=0\ or\ (x - 7)=0[/tex]

Remove brackets

[tex]x + 3=0\ or\ x - 7=0[/tex]

Solve for x

[tex]x =-3\ or\ x =7[/tex]

So, the possible solutions are -3 and 7

Substitute -3 and 7 for x in the original equation to determine the extraneous solution.

[tex]\sqrt{30 - 2x}= x - 3[/tex]

[tex]\sqrt{30 - 2(-3)}= -3 - 3[/tex]

[tex]\sqrt{36}= -6[/tex]

Take square root of 36

[tex]6= -6[/tex]

[tex]\sqrt{30 - 2x}= x - 3[/tex]

[tex]\sqrt{30 - 2(7)}= 7- 3[/tex]

[tex]\sqrt{16}= 4[/tex]

Take square root of 16

[tex]4= 4[/tex]

Hence, the extraneous solution is x = -3, because [tex]6 \ne -6[/tex]

Read more about extraneous solutions at:

https://brainly.com/question/2959656

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