if p=4-q, prove that p3+q3+12pq=64
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Answered by
94
Given,
p = 4-q
Now,
LHS = p³ + q³ + 12pq
= (4-q)³ + q³ + 12(4-q)q
= 64 - q³ - 3×(4)²×q + 3×4×q² + q³ + 48q -12q²
= 64 - 48q + 12q² + 48q - 12q²
= 64
= RHS
p = 4-q
Now,
LHS = p³ + q³ + 12pq
= (4-q)³ + q³ + 12(4-q)q
= 64 - q³ - 3×(4)²×q + 3×4×q² + q³ + 48q -12q²
= 64 - 48q + 12q² + 48q - 12q²
= 64
= RHS
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