Asked by Nickie
What is the solution of the equation?
1+sqrt(3x+3) = sqrt(7x+2)
1+sqrt(3x+3) = sqrt(7x+2)
Answers
Answered by
lisa
x = 2.....
Answered by
Reiny
1 + √(3x+3) = √(7x+2)
square both sides
1 + 2√(3x+3) + 3x+3 = 7x+2
2√(3x+3) = 4x - 2
√(3x+3) = 2x-1
square again:
3x+3 = 4x^2 - 4x + 1
4x^2 - 7x - 2 = 0
(x - 2)(4x + 1) = 0
x = 2 , or x = -1/4
since we squared an equation, all answers MUST be verified in the original equation.
if x = 2
LS = 1 + √9 = 4
RS = √16 = 4
if x = -1/4
LS = 1 + √(9/4) = 5/2
RS = √(1/4) = 1/2 ≠ LS
so the only root is x = 2
square both sides
1 + 2√(3x+3) + 3x+3 = 7x+2
2√(3x+3) = 4x - 2
√(3x+3) = 2x-1
square again:
3x+3 = 4x^2 - 4x + 1
4x^2 - 7x - 2 = 0
(x - 2)(4x + 1) = 0
x = 2 , or x = -1/4
since we squared an equation, all answers MUST be verified in the original equation.
if x = 2
LS = 1 + √9 = 4
RS = √16 = 4
if x = -1/4
LS = 1 + √(9/4) = 5/2
RS = √(1/4) = 1/2 ≠ LS
so the only root is x = 2
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