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?
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Correct answer: C
Explanation
The correct anwer is option 3. (i.e. 158)
By putting z = 0, we get
x + y = z2, xy = 35
x2 + y2 = 2z2 – 2xy = 484 – 70 = 414
(x – y)2 = (x + y)2 – 4xy = 2z2 – 4 × 35 = 344
(x – y)2 + (y – z)2 + (z – x)2
⇒ (x – y)2 + y2 + x2
⇒ 344 + 414 ⇒ 758