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1 vote
A*b= 1
b*c=4
c*d=9
d*e= 16
e*a=25

User Mayqiyue
by
7.6k points

1 Answer

5 votes

Explanation:

To solve the given equations, let's assign variables to each equation and solve them step by step.

Let's assume:

a = x

b = y

c = z

d = w

e = v

From the given equations:

a * b = 1 -> x * y = 1 (Equation 1)

b * c = 4 -> y * z = 4 (Equation 2)

c * d = 9 -> z * w = 9 (Equation 3)

d * e = 16 -> w * v = 16 (Equation 4)

e * a = 25 -> v * x = 25 (Equation 5)

Now, let's solve the equations using substitution:

From Equation 1 (x * y = 1), we can rewrite it as y = 1/x.

Substituting y in Equation 2, we get (1/x) * z = 4, which gives us z = 4x.

Substituting z in Equation 3, we have (4x) * w = 9, which gives us w = 9/(4x).

Substituting w in Equation 4, we get (9/(4x)) * v = 16, which simplifies to v = (16 * 4x)/9.

Finally, substituting v in Equation 5, we have [(16 * 4x)/9] * x = 25.

Simplifying the equation, we get:

(64x^2)/9 = 25.

To solve for x, we can cross multiply and solve the quadratic equation:

64x^2 = 225.

Dividing both sides by 64, we get:

x^2 = 225/64.

Taking the square root of both sides, we have:

x = ±(√(225/64)).

So, x = ±(15/8).

Now, substituting the values of x in the respective equations, we can find the values of y, z, w, and v.

For x = 15/8:

y = 1/(15/8) = 8/15

z = 4 * (15/8) = 30/4 = 15/2

w = 9/(4 * (15/8)) = 9/(30/8) = 9 * (8/30) = 12/5

v = (16 * 4 * (15/8))/9 = (60/2)/9 = 60/18 = 10/3

For x = -15/8:

y = 1/(-15/8) = -8/15

z = 4 * (-15/8) = -30/4 = -15/2

w = 9/(4 * (-15/8)) = 9/(-30/8) = -9 * (8/30) = -12/5

v = (16 * 4 * (-15/8))/9 = (-60/2)/9 = -60/18 = -10/3

Therefore, the possible solutions for the variables are:

x = 15/8, y = 8/15, z = 15/2, w = 12/5, v = 10/3

or

x = -15/8, y = -8/15, z = -15/2, w = -12/5, v = -10/3.

Note: The solution includes both positive and negative values for the variables.

User Rasebo
by
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