Use quadratic formula
(3x/x-1)+(2/x)=4
the solution set is ( , )
(3x/x-1)+(2/x)=4
3x*x + 2(x-1) = 4x(x-1)
3x^2 + 2x-2 = 4x^2-4x
x^2-6x+2 = 0
x = 3±√7
Sg. root (14-5x) = x
Surely you can do this one:
√(14-5x) = x
14-5x = x^2
x^2+5x-14 = 0
(x+7)(x-2) = 0
But watch out for extraneous roots. Check both values in the original equation. Hint
√4 = 2
√4 ≠ -2
To solve the given equation using the quadratic formula, let's re-arrange the equation to have all terms on one side:
(3x/(x-1)) + (2/x) = 4
First, we'll find a common denominator for the two fractions, which is x(x-1). Multiply each term by the common denominator:
[3x * x + 2 * (x-1)] / (x * (x-1)) = 4
Simplifying the numerator:
(3x^2 + 2x - 2) / (x * (x-1)) = 4
Now we have a quadratic equation. We can rewrite it as follows:
3x^2 + 2x - 2 - 4x * (x-1) = 0
Expanding the quadratic term:
3x^2 + 2x - 2 - 4x^2 + 4x = 0
Combine like terms:
-x^2 + 6x - 2 = 0
Now we have a quadratic equation in standard form, ax^2 + bx + c = 0, where a = -1, b = 6, and c = -2. We can use the quadratic formula to find the solutions:
x = (-b ± √(b^2 - 4ac)) / 2a
Substituting the values:
x = (-(6) ± √((6)^2 - 4(-1)(-2))) / 2(-1)
Simplifying further:
x = (-6 ± √(36 - 8)) / (-2)
x = (-6 ± √28) / (-2)
Now, we can simplify the square root:
x = (-6 ± 2√7) / (-2)
Finally, we can simplify the expression by canceling out the negative signs and dividing the numerator and denominator by 2:
x = 3 ± √7
Therefore, the solution set is {3 + √7, 3 - √7}.