Question

if the value of x+y+z=2 and x²+y²+z²=3 and xyz=4 then what's the value of x³+y³+z³​

Answer 1

Answer:

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Step-by-step explanation:

Given x + y + z = 10

(x + y + z) ² = 100

x ² + y ² + z ² + 2 (xy + xz + yz) = 100--------------(1)

Now x ² + y ² + z ² = 38

implies xy + xz + yz = 31

or (xy + xz + yz) ² = (31) ²

using identity x ³ + y ³ + z ³ - 3xyz = (x + y + z) (x ² + y ² + z ²-xy -xz- yz)

= 10 × [38- 31]

= 70

Now x ³ + y ³ + z ³ = 160

or 160- 3xyz = 70

3xyz = 90

xyz = 30