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  4. Solve the equation 3x2-x=25-4x2-x

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Q. Solve the equation $3^{x^{2}-x}=25-4^{x^{2}-x}$

AP EAMCETAP EAMCET 2020

Solution:

Given equation $3^{x^{2}-x}=25-4^{x^{2}-x}$
$\Rightarrow 4^{x^{2}-x}+3^{x^{2}-x}=25=4^{2}+3^{2}$
$\Rightarrow x^{2}-x=2 \Rightarrow x^{2}-x-2=0$
$\Rightarrow (x-2)(x+1)=0 \Rightarrow x=-1,2$