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Hasty.....a^3-(a-8)^3= 344 or8^3+3×8×a(a-8)= 344 or24a(a-8)= 344-512= -168 ora^2-8a+7= 0 ora= 7; 1 and b= -1; -7 solns.
2^3 1^1^2 1^2 (b ➖ 2a+1), 3^2^2^2^2 3^1^1^1^2 3^2(b ➖ 3a+2).
a - b = 8 ⇔ b = a - 8a³ - b³ = 344(a - b)³ = a³ - b³ - 3ab(a - b)8³ = 344 - 3*8ab3*8ab = 344 - 8³3ab = 43 - 8² = 43 - 64 = - 21∴ ab = - 7Recall, b = a - 8a(a - 8) = - 7a² - 8a + 7 = 0(a - 1)(a - 7) = 0∴ a = 1 , 7Recall, b = a - 8∴ b = - 7 , - 1∴ (a , b) = (1 , - 7) , (7 , - 1)
a anb should be natural number, but -1 & -7are not natural numbers. As such solution is not possible
@@kantaseetha2183 please correct and read as not natural number's. .sorry 🙂
Hasty.....a^3-(a-8)^3= 344 or
8^3+3×8×a(a-8)= 344 or
24a(a-8)= 344-512= -168 or
a^2-8a+7= 0 or
a= 7; 1 and b= -1; -7 solns.
2^3 1^1^2 1^2 (b ➖ 2a+1), 3^2^2^2^2 3^1^1^1^2 3^2(b ➖ 3a+2).
a - b = 8 ⇔ b = a - 8
a³ - b³ = 344
(a - b)³ = a³ - b³ - 3ab(a - b)
8³ = 344 - 3*8ab
3*8ab = 344 - 8³
3ab = 43 - 8² = 43 - 64 = - 21
∴ ab = - 7
Recall, b = a - 8
a(a - 8) = - 7
a² - 8a + 7 = 0
(a - 1)(a - 7) = 0
∴ a = 1 , 7
Recall, b = a - 8
∴ b = - 7 , - 1
∴ (a , b) = (1 , - 7) , (7 , - 1)
a anb should be natural number, but -1 & -7are not natural numbers.
As such solution is not possible
@@kantaseetha2183 please correct and read as not natural number's. .sorry 🙂