Given that x +y +z = 3 , X square+ y square +z square equal to 29 , x cube+ y cube+ z cube equal to 45 then find x power 4+ y power 4 +z power4 value?

Question

Answer

Explanation:

Given:

x * y * z = 3

x^2 * y^2 * z^2 = 29

x^3 * y^3 * z^3 = 45

To find:

x^4 * y^4 * z^4 = ?

Solution:

Step 1: Simplify x^3 * y^3 * z^3

We know that x * y * z = 3

So, z = 3 / (x * y)

Substituting the value of z in x^3 * y^3 * z^3, we get:

x^3 * y^3 * (3 / (x * y))^3 = 45

3^3 = 27

Cross-multiplying, we get:

x^6 * y^6 = 15

Step 2: Simplify x^2 * y^2 * z^2

We know that x * y * z = 3

So, z = 3 / (x * y)

Substituting the value of z in x^2 * y^2 * z^2, we get:

x^2 * y^2 * (3 / (x * y))^2 = 29

3^2 = 9

Cross-multiplying, we get:

x^4 * y^4 = 87/9

Step 3: Simplify x^4 * y^4 * z^4

We know that x^6 * y^6 = 15 and x^4 * y^4 = 87/9

Multiplying both equations, we get:

x^10 * y^10 = 261/3

We also know that x * y * z = 3

So, z^2 = 9 / (x^2 * y^2)

Substituting the value of z^2 in x^4 * y^4 * z^4, we get:

x^4 * y^4 * (9 / (x^2 * y^2))^2 = 783/25

Answer:

x^4 * y^4 * z^4 = 783/25

Answer

You can simply use the formula for xpower4+ypower4+zpower4

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