Question

If (x2/yz) + (y2/zx) + (z2/xy) = 3, then what is the value of (x + y + z)3?

Answer 1

if (x²/yz) + (y²/zx) + (z²/xy) = 3
=> x³/xyz + y³/xyz + z³/xyz = 3
=> (x³ + y³ + z³)/xyz = 3
=> x³ + y³ + z³ = 3xyz

we know, when a + b + c = 0 then , a³ + b³ + c³ = 3abc

here, x³ + y³ + z³ = 3xyz then, x + y + z = 0
so, (x + y + z)³ = (0)³ = 0

hence, (x + y + z)³ = 0

Answer 2

answer: 0

thank you!!