Question

Решите пожалуйста. sqrt(2x+sqrt(6x^2+1))=x+1

Answer 1

$sqrt{2x+sqrt{(6x^{2}+1)}}=x+1 \ 2x+sqrt{(6x^{2}+1)}=x^{2}+2x+1 \ sqrt{(6x^{2}+1)}=x^{2}+1 \ 6x^{2}+1=x^{4}+2x^{2}+1 \ x^{4}-4x^{2}=0 \ x^{2}(x^{2}-4)=0 \ x^{2}(x-2)(x+2)=0 \ left[begin{array}{ccc}x=2\x=-2\x=0end$