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25 votes
25 votes
2√3x+1 - √4x+5 =3

show your steps please

User Dan Turner
by
3.1k points

2 Answers

24 votes
24 votes
The answer to your question is 5
User Douglas M
by
2.8k points
16 votes
16 votes

Answer:

x = 5

Explanation:

I'm assuming that 3x +1 & 4x + 5 are all underneath the square root

2 √3x + 1 - √4x + 5 = 3

2 √3x + 1 = 3 + √4x + 5

4 (3x+1) = 9 + 6 √4x + 5 + 4x + 5

12x + 4 = 14 + 6√4x + 5 + 4x

-6 √4x + 5 = 14 + 4x - 12x - 4

-6 √4x + 5 = 10 - 8x

3 √4x + 5 = -5 + 4x (divided both sides by - 2)

9 (4x +5) = 16x^2 - 40x + 25

36x + 45 = 16x^2 - 40x + 25

36x + 45 - 16x^2 + 40x - 25 = 0

76x + 20 - 16x^2 = 0

-16x^2 + 76x + 20 = 0

4x^2 - 19x -5 = 0 (dividied by -4)

4x^2 + x - 20x -5 = 0

x (4x + 1) -5 (4x +1) = 0

(4x +1) (x-5) = 0

Possible answers:

4x + 1 = 0

x - 5 = 0

x = -1/4

x =5

Now we will check which one satisfies the equation

2√3x+1 - √4x+5

Substitue 5 for x and we get 3

Thus we know that 5 is the correct answer

Answered by Gauthmath

User Santosh Tiwari
by
2.8k points
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