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(3+x) = 24/(x+1)
First w need to rewrite th equations. We will get rid of the fraction by multiplying the equation by the denominator.
Let us multuply by (x+1):
==>(3 +x)(x+1) = 24
==> Now open brackets:
=> (3x + 3 + x^2 + x = 24
Now, combine like terms:
==> x^2 + 4x - 21 = 0
Then the equation is quadratic.
If it is written in the original form, it doesn't look like a quadratic equation, but it is.
We have to isolate x to the left side. For this reason, we'll have to multiply both sides by the denominator x+1.
(3 + x)(x + 1) = 24(x + 1)/ (x + 1)
We'll simplify and we'll get:
(3 + x)(x + 1) = 24
We'll remove the brackets:
3x + 3 + x^2 + x - 24 = 0
We'll combine like terms:
x^2 + 4x - 21 = 0
Since the maximum order of the equation is 2, the equation is a quadratic.
The number of the roots is 2 and the formula for finding the roots is:
x1 = [-b+sqrt(b^2 - 4ac)]/2a
x2 = [-b-sqrt(b^2 - 4ac)]/2a
Let's identify a,b,c:
a = 1
b = 4
c = -21
x1 = [-4+sqrt(16+84)]/2
x1 = (-4+10)/2
x1 = 3
x2 = (-4-10)/2
x2 = -7
The given equation 3+x = 24/(x+1) is not a quadratic equation.
A quadratic equation is a second degree polynomial with positive integral powers with real coefficients.
So the given equation is not a quadratic equation, as in ivolves with the negative powers of (x+1) on the right side: 24(x+1)^(-1).
The given equation could be converted into a quadratic equation by multiplying both sides by (x+1):
(3+x)(x+1) = 24 is a 2nd degree polymial equation
3x+3+x^2+3 = 24 is a 2nd degree polynomial equation
x^2+4x+3-24 = 0 is a second degree polynomial equation.
So any second degree polynomial equation is a quadratic equation.
In all these a cannot be zero. b oe c can be zero.
x^2+4x-21 = 0.
So (x-7)(x+3) = 0.
x-7 = 0. x+3 = 0.
x= 7. and x=-3.
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