Mister Exam
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1/x-3^2+3/x-3+4=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
1 3 - - 9 + - - 3 + 4 = 0 x x
$$\left(\left(\left(-9 + \frac{1}{x}\right) + \frac{3}{x}\right) - 3\right) + 4 = 0$$
Detail solution
Given the equation:
$$\left(\left(\left(-9 + \frac{1}{x}\right) + \frac{3}{x}\right) - 3\right) + 4 = 0$$
Use proportions rule:
From a1/b1 = a2/b2 should a1*b2 = a2*b1,
In this case
so we get the equation
$$- \frac{x}{4} = - \frac{1}{8}$$
$$- \frac{x}{4} = - \frac{1}{8}$$
Divide both parts of the equation by -1/4
We get the answer: x = 1/2
$$\left(\left(\left(-9 + \frac{1}{x}\right) + \frac{3}{x}\right) - 3\right) + 4 = 0$$
Use proportions rule:
From a1/b1 = a2/b2 should a1*b2 = a2*b1,
In this case
a1 = 1
b1 = -1/8
a2 = 1
b2 = -x/4
so we get the equation
$$- \frac{x}{4} = - \frac{1}{8}$$
$$- \frac{x}{4} = - \frac{1}{8}$$
Divide both parts of the equation by -1/4
x = -1/8 / (-1/4)
We get the answer: x = 1/2
Sum and product of roots
[src]
sum
1/2
$$\frac{1}{2}$$
=
1/2
$$\frac{1}{2}$$
product
1/2
$$\frac{1}{2}$$
=
1/2
$$\frac{1}{2}$$
1/2