Question

If A 1/A = B 1/B = C 1/C and A BC + B AC + C AB =729 . Then find A 1/A = ?

Answer 1

$A^{1/A} = 9^{1/ABC}$

Step-by-step explanation:

Correction in Question

$if A^{1/A} = B^{1/B} = C^{1/C} , A^{BC} \times B^{AC} \times C^{AB} = 729$

Let say

$A^{1/A} = B^{1/B} = C^{1/C} = k$

Taking power ABC each side then

$if A^{BC} = B^{AC} = C^{AB} =K^{ABC}$

$A^{BC} \times B^{AC} \times C^{AB} = 729\\k^{ABC} \times k^{ABC} \times k^{ABC} = 729\\( k^{ABC})^3 = 729\\( k^{ABC})^3 = 9^3\\ k^{ABC} = 9$

$k = 9^{1/ABC}\\A^{1/A} = 9^{1/ABC}$

Hence

$A^{1/A} = 9^{1/ABC}$

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Answer 2

Hey mate here is your answer

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