Question

If x+y+z=10; x^2+y^2+z^2=20; and x^3+y^3+z^3=40 then what is xyz

Answer 1

Answer:

we know, (x+y+z)² = x²+y²+z²+2(xy+yz+zx)

putting given values we get,

10² = 20+2(xy+yz+zx)

100–20 = 2(xy+yz+zx)

(xy+yz+zx) = 40

now, we also know that,

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

putting values again ,

40-3xyz = 10(20-40)

3xyz = 40+200

xyz = 240/3 = 80 (Ans)

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Answer 2

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we know, (x+y+z)² = x²+y²+z²+2(xy+yz+zx)

putting given values we get,

10² = 20+2(xy+yz+zx)

100–20 = 2(xy+yz+zx)

(xy+yz+zx) = 40

now, we also know that,

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

putting values again ,

40-3xyz = 10(20-40)

3xyz = 40+200

xyz = 240/3 = 80 (Ans)