Question

If x +y +z = 5 and xy + y Z+ZX=9, x^3+ y^3+z^3 - 3xyz = ?​

Answer 1

Step-by-step explanation:

we know that

x³+y³+z³-3xyz=(x+y+z)(x²+y²+z²)-(xy+yz+xz)--A

we also know that

(x+y+z)²=x²+y²+z2+2(xy+yz+zx)---B

putting the values in B first

(5)²=x²+y²+z²+2(9)

25-18=x²+y²+z²

x²+y²+z²=7

now solving eq A

x³+y³+z³-3xyz=(5)(7)-(9)

x³+y³+z³-3xyz=35-9=26