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Solve the following equation and check for extraneous solutions. Show all work. Thank you.

Solve the following equation and check for extraneous solutions. Show all work. Thank-example-1
User Awais Jameel
by
2.4k points

2 Answers

21 votes
21 votes

Answer:


x=19

Explanation:

1) Use this rule:
(x^a)^b=x^a^b .


(x-3)^{(1*1)/(2*2) } =√(x-15)

2) Simplify 1 * 1 to 1.


\sqrt[2*2]{x-3} =√(x-15)

3) Simplify 2 * 2 to 4.


\sqrt[4]{x-3} =√(x-15)

4) Square both sides.


√(x-3) =x-15

5) Square both sides.


x-3=x^2-30x+225

6) Move all terms to one side.


x-3-x^2+30x-225=0

7) Simplify
x-3-x^2+30x-225 to
31x-228-x^2.


31x-228-x^2=0

8) Multiply both sides by -1.


x^2-31x+228=0

9) Factor
x^2-31x+228.

1) Ask: Which two numbers add up to -31 and multiply to 228?


-19 and
-12

2) Rewrite the expression using the above.


(x-19)(x-12)

10) Solve for
x.

1) Ask when will
(x-19)(x-12) equal zero?

When
x-19 =0 or
x-12=0

2) Solve each of the 2 equations above.


x=19,12

11) Check solution.

When
x=12 2, the original equation
\sqrt{√(x-3)}=√(x-15) does not hold true. We will drop
x=12 from the solution set.

12) Therefore,


x=19

Check the Answer:


\sqrt{√(x-3)}=√(x-15)

1) Let
x=19.


\sqrt{√(19-3)}=√(19-15)

2) Simplify 19 - 3 to 16.


\sqrt{√(16)}=√(19-15)

3) Since 4 * 4 is 16 6, the square root of 16 is 4.


√(4)=√(19-15)

4) Since 2 * 2 = 4, the square root of 4 is 2.


2=√(19-15)

5) Simplify 19 - 15 to 4.


2=√(4)

6) Since 2 * 2 = 4, the square root of 4 is 2.


2 = 2

User Strnk
by
3.2k points
8 votes
8 votes
Answer: 19

Hope this helps.
User Shaun Bowe
by
3.5k points