Mathematics
Use property to evaluate:
(i) 93 - 53 - 43
(ii) 383 + (-26)3 + (-12)3
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Answer
(i) By property,
If a + b + c = 0, then
⇒ a3 + b3 + c3 = 3abc
Given,
⇒ 93 - 53 - 43
⇒ 93 + (-5)3 + (-4)3
Let a = 9, b = -5 and c = -4.
∴ a + b + c = 9 + (-5) + (-4) = 9 - 5 - 4 = 0
∴ 93 + (-5)3 + (-4)3 = 3 × 9 × (-5) × (-4) = 540.
Hence, 93 - 53 - 43 = 540.
(ii) By property,
If a + b + c = 0, then
⇒ a3 + b3 + c3 = 3abc
Given,
⇒ 383 + (-26)3 + (-12)3
Let a = 38, b = -26 and c = -12.
∴ a + b + c = 38 + (-26) + (-12) = 38 - 26 - 12 = 0
∴ 383 + (-26)3 + (-12)3 = 3 × 38 × (-26) × (-12) = 35,568.
Hence, 383 + (-26)3 + (-12)3 = 35568.
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