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?
A. 793
B. 681
C. 758
D. 715
Answer: Option C
Solution(By Examveda Team)
x + y + z = 22xy + 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
This Question Belongs to Arithmetic Ability >> Algebra
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