## Related questions with answers

Solve the equation of quadratic form. $x^{4}-10 x^{2}+25=0$

Solution

Verified$\begin{gathered} {x^4} - 10{x^2} + 25 = 0 \\ \textcolor{#4257b2}{ {\text{Write the equation in quadratic form}}} \\ {\left( {{x^2}} \right)^2} - 10\left( {{x^2}} \right) + 25 = 0 \\ \textcolor{#4257b2}{ {\text{Let }}u = {x^2},{\text{ so}}} \\ \underbrace {{{\left( {{x^2}} \right)}^2} - 10\left( {{x^2}} \right) + 25 = 0}_ \Downarrow \\ {u^2} - 10u + 25 = 0 \\ \textcolor{#4257b2}{{\text{Factor the trinomial}}} \\ {\left( {u - 5} \right)^2} = 0 \\ \textcolor{#4257b2}{ {\text{Set the factor equal to 0}}} \\ u - 5 = 0 \Rightarrow u = 5 \\ \textcolor{#4257b2}{ {\text{Back - substitute }}u = {x^2}{\text{ and solve for }}x} \\ {x^2} = 5 \\ \textcolor{#4257b2}{{\text{Therefore}}{\text{,}}} \\ \sqrt {{x^2}} = \pm \sqrt 5 \\ x = \pm \sqrt 5 \\ \end{gathered}$

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