Question
Download Solution PDFIf x = 222, y = 223 and z = 224, then find the value of x3 + y3 + z3 - 3xyz.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
x = 222,
y = 223
z = 224
Formula used:
x3 + y3 + z3 - 3xyz = (1/2)(x + y + z)[(x - y)2 + (y - z)2 + (z - x)2]
Calculation:
x3 + y3 + z3 - 3xyz = (1/2)(222 + 223 + 224)[(222 - 223)2 + (223 - 224)2 + (224 - 222)2]
⇒ x3 + y3 + z3 - 3xyz = (1/2)(669)[(1) + (1) + (4)]
⇒ x3 + y3 + z3 - 3xyz = 3 × 669
⇒ x3 + y3 + z3 - 3xyz = 2007
∴ The value of x3 + y3 + z3 - 3xyz is 2007.
Last updated on Jul 14, 2025
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