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

$$$$$$$$$$\mathrm{If}{\mathrm{a}}^{\mathrm{b}}={\mathrm{b}}^{\mathrm{a}}\mathrm{and}\mathrm{a}=2\mathrm{b}\mathrm{then}\mathrm{find}\mathrm{the}$$$$\mathrm{value}\mathrm{of}{\mathrm{a}}^2+{\mathrm{b}}^2.$$

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

$$\Rightarrow {\left(2b\right)}^b=b^{2b}$$$$\Rightarrow b^b(2^b-b^b)=0$$$$sinceb\ne 0cause\Rightarrow a=0and{0}^{0}notdefind$$$$\Rightarrow 2^b-b^b=0\Rightarrow bln\left(2\right)=bln\left(b\right)\Rightarrow b(ln\left(2\right)-ln\left(b\right))=0$$$$\Rightarrow b=2\Rightarrow a=4$$$$a^2+b^2=4+16=20$$

Commented by niroj last updated on 21/Feb/20

$$thankyou.$$

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