Solve (sqrt2x-3)-(3sqrt1-x)=0
Hmmm. I saw you answered a question on trig, but this one bothers you?
√(2x-3) - 3√(1-x) = 0
√(2x-3) = 3√(1-x)
2x-3 = 9-9x
11x = 12
x = 12/11
Now, see whether that works in the original equation.
It does not, since 2x-3 < 0
Thanks for helping me, algebra is just my weakness 😓
To solve the equation (sqrt(2x)-3)-(3sqrt(1-x))=0, we need to isolate the variable x.
Step 1: Remove the parentheses by applying the distributive property:
sqrt(2x) - 3 - 3sqrt(1-x) = 0
Step 2: Combine like terms:
sqrt(2x) - 3sqrt(1-x) - 3 = 0
Step 3: Move the constant term (-3) to the other side of the equation:
sqrt(2x) - 3sqrt(1-x) = 3
Step 4: To remove square roots, we need to square both sides of the equation:
(sqrt(2x))^2 - 2(sqrt(2x))(3sqrt(1-x)) + (3sqrt(1-x))^2 = 3^2
2x - 6sqrt(2x)(sqrt(1-x)) + 9(1-x) = 9
Step 5: Simplify each term:
2x - 6sqrt(2x)(sqrt(1-x)) + 9 - 9x = 9
2x - 9x - 6sqrt(2x)(sqrt(1-x)) + 9 = 9
-7x - 6sqrt(2x)(sqrt(1-x)) = 0
Step 6: Move the constant term (9) to the other side of the equation:
-7x - 6sqrt(2x)(sqrt(1-x)) = -9
Step 7: Divide both sides of the equation by -1 to switch the signs:
7x + 6sqrt(2x)(sqrt(1-x)) = 9
Step 8: Divide both sides of the equation by 7:
x + (6/7)sqrt(2x)(sqrt(1-x)) = 9/7
Step 9: Move the term with the square roots to the other side of the equation:
x = 9/7 - (6/7)sqrt(2x)(sqrt(1-x))
Now, to further solve for x, we can apply numerical methods, such as using a calculator or approximation techniques. Unfortunately, this equation does not have a simple algebraic solution.