4. REVIEW PROBLEM: Solve).
√3-2x + √3x +13 =5
the term (3-2x) is under a radical as well as the term (3x+13). Please show all steps!! i keep on getting x=9 but plugging it in it is wrong!
yes, x=9 will certainly not work.
√(3-2x) + √(3x+13) = 5
√(3-2x) = 5 - √(3x+13)
3-2x = 25 - 10√(3x+13) + 3x+13
35+5x = 10√(3x+13)
x+7 = 2√(3x+13)
x^2+14x+49 = 12x+52
x^2+2x-3 = 0
(x+3)(x-1) = 0
x = 1 or -3
check
x=1: √1 + √16 = 5
x=-3: √9 + √4 = 5
yep.
To solve the given equation, √3-2x + √3x + 13 = 5, where both (3-2x) and (3x+13) are under a radical, follow the steps below:
Step 1: Isolate the radical terms on one side of the equation.
Start by subtracting 5 from both sides to bring the constant term to the right side:
√3 - 2x + √3x + 13 - 5 = 0
√3 - 2x + √3x + 8 = 0
Step 2: Rearrange the terms to group the radical terms together.
√3 + √3x - 2x + 8 = 0
Step 3: Combine like terms.
To simplify further, combine the terms containing x:
(√3 - 2)x + √3 + 8 = 0
Step 4: Solve for x by isolating the term containing x.
Subtract (√3 + 8) from both sides to isolate the term containing x:
(√3 - 2)x = -√3 - 8
Step 5: Divide both sides by (√3 - 2) to solve for x.
x = (-√3 - 8) / (√3 - 2)
Now, to verify whether x = 9 is a correct solution, substitute this value into the equation and check the result:
√3 - 2(9) + √3(9) + 13 = 5
Performing the calculations,
√3 - 18 + 3√3 + 13 = 5
16√3 - 5 = 5
16√3 = 10
√3 = 10/16
√3 = 5/8
Since 5/8 is not equal to √3, we can conclude that x = 9 is not the correct solution to the equation.