Question

यदि x² + y² + z² = 20 व x + y + z = 0, तब सिद्ध कीजिए xy + yz + zx = -10

Answer 1

x + y + z = 0

वर्ग करने पर, (x + y + z)² = 0

x² + y² + z² + 2(xy + yz + zx) = 0

20 + 2(xy + yz + zx) = 0

2(xy + yz + zx) = 0 – 20 = -20

xy + yz + zx = -20/2 = -10