A.P. के तीन संख्याओं का योग 12 है तथा उनके पन का योग 408 है। संख्याओं को ज्ञात कीजिए।
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1 , 4 , 7 or 7 , 4 , 1 A.P. के तीन संख्या योग 12 है तथा उनके घन का योग 408 है
Step-by-step explanation:
Correction 408 should be 48
तीन संख्या
a - d , a , a + d
A.P. के तीन संख्याओं का योग 12 है
=> (a - d) + a + (a + d) = 12
=> 3a = 12
=> a = 4
घन का योग 408 है
(a - d)³ + a³ + (a + d)³ = 408
=> (4- d)³ + 4³ + (4 + d)³ = 408
=> 4³ - d³ - 12d(4 - d) + 4³ + 4³ + d³ + 12d(4 + d) = 408
=> -48d + 12d² + 48d + 12d² = 216
=> 24d² = 216
=> d² = 9
=> d = ±3
1 , 4 , 7 or 7 , 4 , 1
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