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Rom4ik [11]
3 years ago
5

X^4 + 25 = 26x^2please answer quick. I'll give brainliest rothe first person​

Mathematics
1 answer:
Shalnov [3]3 years ago
7 0

{ \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}}}}

{ \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}}}}

{ \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}}}

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