Question

please solve this question ​

Answer 1

Answer:

$a^{2x}(a^2+1)=(a^{3x}+a^x)a\\\\\implies a^{2x}.a^2+a^{2x}=a^{3x}.a+a^x.a\\\\\implies a^{2x+2}+a^{2x}=a^{3x+1}+a^{x+1}\\\\\implies a^{(2x+2).(2x)}=a^{(3x+1)(x+1)}\\\\\implies a^{4x^2+4x}=a^{3x^2+3x+x+1}\\\\\implies \bold{a^{4x^2+4x}=a^{3x^2+4x+1}}$

Now bases are equal . So exponents must be equal.

$\implies 4x^2+4x=3x^2+4x+1\\\\\implies x^2=1\\\\\implies \bf{\red{\bold{x =\pm 1}}}$