?
If x + y + z = 22 and xy + yz + zx = 35, then what is the value of (x - y)2 + (y - z)2 + (z - x)2?
Answer & Solution
Correct Answer:
Option
C
x + y + z = 22
xy + yz + zx = 35
(x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx)
(22)2 = x2 + y2 + z2 + 2 × 35
484 - 70 = x2 + y2 + z2
x2 + y2 + z2 = 414
(x - y)2 + (y - z)2 + (z - x)2
= 2(x2 + y2 + z2 - xy - yz - zx)
= 2(414 - 35)
= 2 × 379
= 758
xy + yz + zx = 35
(x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx)
(22)2 = x2 + y2 + z2 + 2 × 35
484 - 70 = x2 + y2 + z2
x2 + y2 + z2 = 414
(x - y)2 + (y - z)2 + (z - x)2
= 2(x2 + y2 + z2 - xy - yz - zx)
= 2(414 - 35)
= 2 × 379
= 758
Join the Discussion
Login to post a comment or share your explanation.
Login