If-a-b-b-a-and-a-2b-then-find-the-value-of-a-2-b-2-

Question Number 82489 by niroj last updated on 21/Feb/20

If a^{b} = b^{a} and a = 2 b then find the

value of a^{2} + b^{2} .

Answered by mind is power last updated on 21/Feb/20

\Rightarrow {(2 b)}^{b} = b^{2 b}

\Rightarrow b^{b} (2^{b} - b^{b}) = 0

s i n c e b \neq 0 c a u s e \Rightarrow a = 0 a n d 0^{0} n o t d e f i n d

\Rightarrow 2^{b} - b^{b} = 0 \Rightarrow b l n (2) = b l n (b) \Rightarrow b (l n (2) - l n (b)) = 0

\Rightarrow b = 2 \Rightarrow a = 4

a^{2} + b^{2} = 4 + 16 = 20

Commented by niroj last updated on 21/Feb/20

t h a n k y o u .

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