Mister Exam
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- Equation:
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Equation 6*x^2+x-7=0
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Equation 2x^2-x+3=0
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Equation 11x-6x+17=2042
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Equation (2*x-1)/(x-1)^2=0
- Express {x} in terms of y where:
- -12*x+2*y=16
- 17*x+19*y=-14
- 14*x+7*y=19
- -16*x-8*y=2
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Identical expressions
- two *a- seven *b+ five / seven *a- two *b+ five = nine
- 2 multiply by a minus 7 multiply by b plus 5 divide by 7 multiply by a minus 2 multiply by b plus 5 equally 9
- two multiply by a minus seven multiply by b plus five divide by seven multiply by a minus two multiply by b plus five equally nine
- 2a-7b+5/7a-2b+5=9
- 2*a-7*b+5 divide by 7*a-2*b+5=9
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Similar expressions
- 2*a+7*b+5/7*a-2*b+5=9
- 2*a-7*b+5/7*a+2*b+5=9
- 2*a-7*b-5/7*a-2*b+5=9
- 2*a-7*b+5/7*a-2*b-5=9
2*a-7*b+5/7*a-2*b+5=9 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
5*a
2*a - 7*b + --- - 2*b + 5 = 9
7
$$\left(- 2 b + \left(\frac{5 a}{7} + \left(2 a - 7 b\right)\right)\right) + 5 = 9$$
Detail solution
Given the linear equation:
Looking for similar summands in the left part:
Move free summands (without b)
from left part to right part, we given:
$$\frac{19 a}{7} - 9 b = 4$$
Move the summands with the other variables
from left part to right part, we given:
$$\left(-9\right) b = \frac{\left(-19\right) a}{7} + 4$$
Divide both parts of the equation by -9
We get the answer: b = -4/9 + 19*a/63
2*a-7*b+5/7*a-2*b+5 = 9
Looking for similar summands in the left part:
5 - 9*b + 19*a/7 = 9
Move free summands (without b)
from left part to right part, we given:
$$\frac{19 a}{7} - 9 b = 4$$
Move the summands with the other variables
from left part to right part, we given:
$$\left(-9\right) b = \frac{\left(-19\right) a}{7} + 4$$
Divide both parts of the equation by -9
b = 4 - 19*a/7 / (-9)
We get the answer: b = -4/9 + 19*a/63
The graph
Sum and product of roots
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sum
4 19*re(a) 19*I*im(a) - - + -------- + ---------- 9 63 63
$$\frac{19 \operatorname{re}{\left(a\right)}}{63} + \frac{19 i \operatorname{im}{\left(a\right)}}{63} - \frac{4}{9}$$
=
4 19*re(a) 19*I*im(a) - - + -------- + ---------- 9 63 63
$$\frac{19 \operatorname{re}{\left(a\right)}}{63} + \frac{19 i \operatorname{im}{\left(a\right)}}{63} - \frac{4}{9}$$
product
4 19*re(a) 19*I*im(a) - - + -------- + ---------- 9 63 63
$$\frac{19 \operatorname{re}{\left(a\right)}}{63} + \frac{19 i \operatorname{im}{\left(a\right)}}{63} - \frac{4}{9}$$
=
4 19*re(a) 19*I*im(a) - - + -------- + ---------- 9 63 63
$$\frac{19 \operatorname{re}{\left(a\right)}}{63} + \frac{19 i \operatorname{im}{\left(a\right)}}{63} - \frac{4}{9}$$
-4/9 + 19*re(a)/63 + 19*i*im(a)/63
Rapid solution
[src]
4 19*re(a) 19*I*im(a)
b1 = - - + -------- + ----------
9 63 63
$$b_{1} = \frac{19 \operatorname{re}{\left(a\right)}}{63} + \frac{19 i \operatorname{im}{\left(a\right)}}{63} - \frac{4}{9}$$
b1 = 19*re(a)/63 + 19*i*im(a)/63 - 4/9