Magic of Math #3

Algebra Level 1

If k k is a positive integer such that there exist a number A A such that k = A + A = A × A = A A k = A+A = A\times A = A^A , find the value of A k \dfrac Ak .


The answer is 0.5.

Magic Math by Magic Math , 21, Thailand

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4 solutions

Department 8
Aug 26, 2015

A + A = k 2 A = k A k = 1 2 A+A=k \\ 2A=k \\ \frac{A}{k}=\frac{1}{2}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Easiest Method there.

Mehul Arora - 5 years, 9 months ago
Shyam Gupta
Aug 26, 2015

A^2=k

2A=k

solving these we get A=2 and k=4..

sp (2/4) will give 0.5

2 Helpful 0 Interesting 0 Brilliant 0 Confused

K=2A=A^2=A^A So A=2 K=2*2=4 A/K=0.5 ควย

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Azadali Jivani
Sep 1, 2015

A + A = A* A
2A - A² = 0
A(2 - A) = 0
So A = 2
k = 2 + 2 = 4
So A/k = 2/4 = 0.5




0 Helpful 0 Interesting 0 Brilliant 0 Confused

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