Mister Exam
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How to use it?
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Equation 2-3(7+2x)=11
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Identical expressions
- three √(x- seven)= four
- 3√(x minus 7) equally 4
- three √(x minus seven) equally four
- 3√x-7=4
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Similar expressions
- 3√(x+7)=4
3√(x-7)=4 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$3 \sqrt{x - 7} = 4$$
Because equation degree is equal to = 1/2 - does not contain even numbers in the numerator, then
the equation has single real root.
We raise the equation sides to 2-th degree:
We get:
$$3^{2} \left(\sqrt{x - 7}\right)^{2} = 4^{2}$$
or
$$9 x - 63 = 16$$
Move free summands (without x)
from left part to right part, we given:
$$9 x = 79$$
Divide both parts of the equation by 9
We get the answer: x = 79/9
The final answer:
$$x_{1} = \frac{79}{9}$$
$$3 \sqrt{x - 7} = 4$$
Because equation degree is equal to = 1/2 - does not contain even numbers in the numerator, then
the equation has single real root.
We raise the equation sides to 2-th degree:
We get:
$$3^{2} \left(\sqrt{x - 7}\right)^{2} = 4^{2}$$
or
$$9 x - 63 = 16$$
Move free summands (without x)
from left part to right part, we given:
$$9 x = 79$$
Divide both parts of the equation by 9
x = 79 / (9)
We get the answer: x = 79/9
The final answer:
$$x_{1} = \frac{79}{9}$$
Sum and product of roots
[src]
sum
79/9
$$\frac{79}{9}$$
=
79/9
$$\frac{79}{9}$$
product
79/9
$$\frac{79}{9}$$
=
79/9
$$\frac{79}{9}$$
79/9
Numerical answer
[src]
x1 = 8.77777777777778
x2 = 8.77777777777795 + 5.6555284236465e-13*i
x3 = 8.77777777777778 + 6.19762242122728e-15*i
x4 = 8.77777777777778 + 3.90949647667852e-17*i
x4 = 8.77777777777778 + 3.90949647667852e-17*i