Question

sqrt(2*x+sqrt(6*x^2-1))=x+1

Answer 1

$\sqrt{2x + \sqrt{6 {x}^{2} - 1} } = x + 1$

$( { \sqrt{2x + \sqrt{6 {x}^{2} - 1 } } )}^{2} = ({x + 1})^{2}$

$2x + \sqrt{6 {x}^{2} - 1 } = {x}^{2} + 2x + 1$

$\sqrt{6 {x}^{2} - 1 } = {x}^{2} + 1$

$( { \sqrt{6 {x}^{2} - 1 }) }^{2} = {x}^{4} + 2 {x}^{2} + 1$

$6 {x}^{2} - 1 = {x}^{4} + {x}^{2} + 1$

${x}^{4} - 5 {x}^{2} + 2 = 0$