Mister Exam
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How to use it?
- Equation:
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Equation sinx=1
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Equation x^2+5*x-14=0
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Equation -2*x-7=-4*x
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Equation x+4|x|=3
- Express {x} in terms of y where:
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Identical expressions
- x*|x|+ three *|x|+ six + two *x= three
- x multiply by module of x| plus 3 multiply by |x| plus 6 plus 2 multiply by x equally 3
- x multiply by module of x| plus three multiply by |x| plus six plus two multiply by x equally three
- x|x|+3|x|+6+2x=3
-
Similar expressions
- x*|x|+3*|x|-6+2*x=3
- x*|x|+3*|x|+6-2*x=3
- x*|x|-3*|x|+6+2*x=3
x*|x|+3*|x|+6+2*x=3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
x*|x| + 3*|x| + 6 + 2*x = 3
$$2 x + \left(\left(x \left|{x}\right| + 3 \left|{x}\right|\right) + 6\right) = 3$$
Detail solution
For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$x \geq 0$$
$$x \geq 0$$
or
$$0 \leq x \wedge x < \infty$$
we get the equation
$$x x + 2 x + 3 x + 3 = 0$$
after simplifying we get
$$x^{2} + 5 x + 3 = 0$$
the solution in this interval:
$$x_{1} = - \frac{5}{2} - \frac{\sqrt{13}}{2}$$
but x1 not in the inequality interval
$$x_{2} = - \frac{5}{2} + \frac{\sqrt{13}}{2}$$
but x2 not in the inequality interval
2.
$$x \geq 0$$
$$x < 0$$
The inequality system has no solutions, see the next condition
3.
$$x < 0$$
$$x \geq 0$$
The inequality system has no solutions, see the next condition
4.
$$x < 0$$
$$x < 0$$
or
$$-\infty < x \wedge x < 0$$
we get the equation
$$- x x + 3 \left(- x\right) + 2 x + 3 = 0$$
after simplifying we get
$$- x^{2} - x + 3 = 0$$
the solution in this interval:
$$x_{3} = - \frac{1}{2} + \frac{\sqrt{13}}{2}$$
but x3 not in the inequality interval
$$x_{4} = - \frac{\sqrt{13}}{2} - \frac{1}{2}$$
The final answer:
$$x_{1} = - \frac{\sqrt{13}}{2} - \frac{1}{2}$$
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$x \geq 0$$
$$x \geq 0$$
or
$$0 \leq x \wedge x < \infty$$
we get the equation
$$x x + 2 x + 3 x + 3 = 0$$
after simplifying we get
$$x^{2} + 5 x + 3 = 0$$
the solution in this interval:
$$x_{1} = - \frac{5}{2} - \frac{\sqrt{13}}{2}$$
but x1 not in the inequality interval
$$x_{2} = - \frac{5}{2} + \frac{\sqrt{13}}{2}$$
but x2 not in the inequality interval
2.
$$x \geq 0$$
$$x < 0$$
The inequality system has no solutions, see the next condition
3.
$$x < 0$$
$$x \geq 0$$
The inequality system has no solutions, see the next condition
4.
$$x < 0$$
$$x < 0$$
or
$$-\infty < x \wedge x < 0$$
we get the equation
$$- x x + 3 \left(- x\right) + 2 x + 3 = 0$$
after simplifying we get
$$- x^{2} - x + 3 = 0$$
the solution in this interval:
$$x_{3} = - \frac{1}{2} + \frac{\sqrt{13}}{2}$$
but x3 not in the inequality interval
$$x_{4} = - \frac{\sqrt{13}}{2} - \frac{1}{2}$$
The final answer:
$$x_{1} = - \frac{\sqrt{13}}{2} - \frac{1}{2}$$
Sum and product of roots
[src]
sum
____ 1 \/ 13 - - - ------ 2 2
$$- \frac{\sqrt{13}}{2} - \frac{1}{2}$$
=
____ 1 \/ 13 - - - ------ 2 2
$$- \frac{\sqrt{13}}{2} - \frac{1}{2}$$
product
____ 1 \/ 13 - - - ------ 2 2
$$- \frac{\sqrt{13}}{2} - \frac{1}{2}$$
=
____ 1 \/ 13 - - - ------ 2 2
$$- \frac{\sqrt{13}}{2} - \frac{1}{2}$$
-1/2 - sqrt(13)/2
Rapid solution
[src]
____
1 \/ 13
x1 = - - - ------
2 2
$$x_{1} = - \frac{\sqrt{13}}{2} - \frac{1}{2}$$
x1 = -sqrt(13)/2 - 1/2