Question

If a, b, c and d are four odd perfect cube numbers, then which of the following is always a factor of (3under root a + 3under root b) whole square , (3under root c + 3under root d)?
Vvvvvery very urgent

Answer 1

(∛a + ∛b)² (∛c + ∛d)

2) 8

let us check imagine 4 odd cubic numbers as 1, 3, 5, 7

(1 + 3)² (5 + 7) = 16 x 12    (8 comes as factor)

(1+5)² (3 +7) = 36 x 10   (8comes as factor)

(1+7)² (3+5) = 64 x 8  (8 comes as factor)

Answer 2

Thank you for asking this question. Here is your answer:

a = 1

b = 8

c = 125

d = 343

These are the four odd perfect cube numbers.

∛a=∛1=1,∛b=∛8=2,∛c=∛125=5  and ∛d=∛343=7  

(∛a+∛b)^2 (∛c  ∛d) will be 192, 360, 512, 576 and 600

(192, 360, 512, 576, 600) = 8

So this means that 8 will always be the factor of (∛a+∛b)^2 (∛c+∛d)

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