Question

If a^b= b^a and a = 2b then find the value of a^2+b^2

a) 20
b) 30
c) 28
d) 24
​

Answer 1

`\large \boxed{\sf \bf \ \ a^2+b^2=20 \ \ }`

Explanation:

Hello, please consider the following.

`a^b=b^a\\\\\text{ We can replace a by 2b.}\\\\(2b)^b=2^b\cdot b^b=b^(2a)=b^2\cdot b^b\\\\\text{ Let's assume that b is different from 0 and we can divide by }b^b \\ \\ \text{ both sides of the equation, and it come.}\\\\2^b=b^2\\\\\text{ We find b = 2 and then a = 4, So}\\\\a^2+b^2=4^2+2^2=16+4=20`

Hope this helps.

Do not hesitate if you need further explanation.

Thank you