+0  
 
Sort: 

1+0 Answers

 #1
avatar
0

Solve for x:
2 + sqrt(2 x + 3) = sqrt(6 x + 7)

Raise both sides to the power of 2:
(2 + sqrt(2 x + 3))^2 = 6 x + 7

Subtract 6 x + 7 from both sides:
-7 - 6 x + (2 + sqrt(2 x + 3))^2 = 0

-7 - 6 x + (2 + sqrt(2 x + 3))^2 = 4 sqrt(2 x + 3) - 4 x:
4 sqrt(2 x + 3) - 4 x = 0

Simplify and substitute y = sqrt(2 x + 3):
 4 sqrt(2 x + 3) - 4 x = 6 + 4 sqrt(2 x + 3) - 2 (sqrt(2 x + 3))^2 = -2 y^2 + 4 y + 6 = 0:
-2 y^2 + 4 y + 6 = 0

The left hand side factors into a product with three terms:
-2 (y - 3) (y + 1) = 0

Divide both sides by -2:
(y - 3) (y + 1) = 0

Split into two equations:
y - 3 = 0 or y + 1 = 0

Add 3 to both sides:
y = 3 or y + 1 = 0

Substitute back for y = sqrt(2 x + 3):
sqrt(2 x + 3) = 3 or y + 1 = 0

Raise both sides to the power of two:
2 x + 3 = 9 or y + 1 = 0

Subtract 3 from both sides:
2 x = 6 or y + 1 = 0

Divide both sides by 2:
x = 3 or y + 1 = 0

Subtract 1 from both sides:
x = 3 or y = -1

Substitute back for y = sqrt(2 x + 3):
x = 3 or sqrt(2 x + 3) = -1

Raise both sides to the power of two:
x = 3 or 2 x + 3 = 1

Subtract 3 from both sides:
x = 3 or 2 x = -2

Divide both sides by 2:
x = 3 or x = -1

2 + sqrt(2 x + 3) ⇒ 2 + sqrt(3 + 2 (-1)) = 3
sqrt(6 x + 7) ⇒ sqrt(7 + 6 (-1)) = 1:
So this solution is incorrect

2 + sqrt(2 x + 3) ⇒ 2 + sqrt(3 + 2 3) = 5
sqrt(6 x + 7) ⇒ sqrt(7 + 6 3) = 5:
So this solution is correct

The solution is:
Answer: |x = 3

Guest Mar 5, 2017

8 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details