help me
the question about algebra
➡️do not inconsequential and must with and must be accompanied by steps for the process
thanks
Answers
9514 1404 393
Answer:
(x, y, z) = (8√7/105, 2√7/21, 4√7/35)
Step-by-step explanation:
The algebra is straightforward, if tedious.
We'll define X = x^2, Y = y^2, Z = z^2, -1/16 = a, -1/25 = b, -1/36 = c. Then the equations become ...
√X = √(Y +a) +√(Z +a) . . . . [eq1]
√Y = √(Z +b) +√(X +b) . . . . [eq2]
√Z = √(X +c) +√(Y +c) . . . . [eq3]
__
As with any radical equation, you square both sides, isolate the remaining radical, then square both sides again. Each squaring introduces extraneous solutions.
The equations are symmetrical, so we can do the tedious stuff on the first one, then make the appropriate substitutions to see the other two equations.
X = Y +a + 2√((Y+a)(Z+a)) +Z +a
X - Y - Z -2a = 2√((Y+a)(Z+a)) . . . . isolate the remaining radical
(X -Y -Z -2a)^2 = 4(Y+a)(Z+a) . . . . square both sides again
X^2 +Y^2 +Z^2 +4a^2 -2XY -2XZ +2YZ -4aX +4aY +4aZ = 4YZ +4aY +4aZ +4a^2
Subtracting the right side gives ...
X^2 +Y^2 +Z^2 -2XY -2XZ -2YZ -4aX = 0 . . . . [eq4]
Then the remaining equations are ...
X^2 +Y^2 +Z^2 -2XY -2XZ -2YZ -4bY = 0 . . . . [eq5]
X^2 +Y^2 +Z^2 -2XY -2XZ -2YZ -4cZ = 0 . . . . [eq6]
Subtracting [eq6] from [eq5] gives a relation between Y and Z:
-4bY +4cZ = 0
Z = bY/c . . . . [eq7]
Substituting this into [eq4], we have ...
X^2 +Y^2 +(bY/c)^2 -2XY -2X(bY/c) -2Y(bY/c) -4aX = 0
X^2 +Y^2(1 -2b/c +(b/c)^2) -2XY(1 +b/c) -4aX = 0 . . . . [eq8]
Subtracting [eq5] from [eq4] gives a relation between X and Y:
-4aX +4bY = 0
Y = aX/b . . . . [eq9]
Substituting this into [eq8], we have ...
X^2 +(aX/b(1 -b/c))^2 -2X(aX/b)(1 +b/c) -4aX = 0
Dividing by X* gives a linear equation in X:
X(1 +(a/b(1 -b/c))^2 -2a/b(1+b/c)) -4a = 0
X = 4a/(1 +(a/b(1 -b/c))^2 -2a/b(1+b/c))
Substituting the above values for a, b, c, we have ...
X = 64/1575
x = √X = √(64/1575) = 8/(15√7)
Y = X(25/16)
y = x(5/4) = 2/(3√7)
Z = Y(36/25)
z = y(6/5) = 4/(5√7)
The solution is ...
x = 8√7/105 ≈ 0.201581y = 2√7/21 ≈ 0.251976z = 4√7/35 ≈ 0.302372_____
* At this point the equation is of the form pX^2 +qX = 0 or X(pX +q) = 0. One solution is X=0, which is extraneous. The solution of interest is X = -q/p.
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Answer:
ANSWER
GIVEN:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
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Answers
Answer:
10g+6 is the answer
Step-by-step explanation:
According to the synthetic division below, which of the following statements
are true?
Check all that apply.
Answers
The question is not complete, so i have attached it.
Answer:
Options A, B & E are correct
Step-by-step explanation:
In the synthetic division attached, we see that:
: 2 , -2 & -12 are the coefficient of the dividend of the function 2x² - 2x - 12
: The divisor is 3
Thus;
x = 3 is a root of f(x) = 2x² - 2x - 12
Thus, (x - 3) is a factor of the dividend which is the function f(x) = 2x² - 2x - 12
- Now, from the attached image, the coefficients of the quotient are 2 , 4
- The quotient will be 1 degree less than the dividend since it was divided by the factor (x - 3)
The degree of the dividend will be 2 since it contains x²
Thus, the degree of the quotient will be 1
Therefore, the quotient in factor form is (2x + 4)
Looking at the given statements in the options;
- Option A is true, because we have established earlier that 3 is a root of f(x) = 2x² - 2x - 12
- Option B is true because we have established that (x - 3) is a factor of 2x² - 2x - 12
- Option C is not true because the factor is (x + 3) and not (x - 3)
-Option D is not true because the root is 3 and not -3
- Option E is true because we have established that quotient as a factor is: (2x + 4)
Thus, the correct options are A , B , E