The sum of three numbers in AP is 12 and the sum of their cubes is 288.
Find the numbers.
4
तीन संख्याओं, जो समांतर श्रेढ़ी में हैं, का योगफल 12 है तथा उनके घनों का योगफल 288 है। संख्याएँ
जात कीजिए।
Answers
Answer:
2,4,6
Step-by-step explanation:
Let, the three numbers are a, b and c.
Since they are in AP.
Therefore, we have,
=> a + c = 2b
Also, given that,
Their sum is 12.
=> a + b + c = 12
=> 2b + b = 12
=> 3b = 12
=> b = 12/3
=> b = 4
Therefore, we have,
=> a + c = 2(4) = 8
Again, It's given that,
Sum of their cubes = 288
=> a^3 + b^3 + c^3 = 288
=> a^3 + 4^3 + c^3 = 288
=> a^3 + 64 + c^3 = 288
=> a^3 + c^3 = 288 - 64
=> a^3 + c^3 = 224
=> (a+c)(a^2 + c^2 - ac ) = 224
=> 8{(a+c)^2 - 2ac - ac} = 224
=> 8^2 - 3ac = 224/8
=> 64 - 3ac = 28
=> 3ac = 64-28
=> 3ac = 36
=> ac = 36/3
=> ac = 12
=> a = 12/c
Therefore, we will get,
=> 12/c + c = 8
=> (12+c^2)/c = 8
=> c^2 + 12 = 8c
=> c^2 - 8c + 12 = 0
=> c^2 - 6c - 2c + 12 = 0
=> c(c-6) -2(c-6) = 0
=> (c-6)(c-2) = 0
=> c = 6, 2
Therefore, we have,
=> a = 12/6, 12/2 = 2, 6
Hence, the required numbers are 2,4 and 6.
Step-by-step explanation:
hope it helps.......!!!!!
