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x^4 + 25 = 26x^2

please answer quick. I'll give brainliest rothe first person​

Sagot :

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[tex]{ \leadsto{ \sf{ \green{ {x}^{4} + 25 = 26 {x}^{2} }}}} \\ \\ { \leadsto{ \sf{ \green{ {x}^{4} - 26 {x}^{2} + 25 = 0}}}} \\ \\ { \sf{ \underline{ \blue{let \: \: {x}^{2} \: be \: equal \: to \: a}}}}[/tex]

[tex]{ \leadsto { \green{ \sf{ {a}^{2} - 26a + 25 = 0}}}} \\ \\ { \leadsto{ \green{ \sf{ {a}^{2} - (a + 25a) + 25 = 0}}}} \\ \\ { \leadsto{ \green{ \sf{ {a}^{2} - a - 25a + 25 = 0}}}} \\ \\ { \leadsto{ \green{ \sf{a(a - 1) - 25(a - 1) = 0}}}}[/tex]

[tex]{ \leadsto{ \sf{ \green{(a - 1)(a - 25) = 0}}}} \\ \\ { \sf{ substituting \: value \: of \: a}} \\ \\ { \rightarrow{ \sf{ \blue{( {x}^{2} - 1)( {x}^{2} - 25) = 0}}}} \\ \\ { \sf {{x}^{2} = 1}} \\ { \sf{ \underline{x = \: ± \: 1}}} \\ \\ \\ { \sf {x}^{2} = 25} \\ { \sf{ \underline{x = \: ± \: 5}}}[/tex]

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