Biquadratic

By introducing a new variable, solve the biquadratic equation:

−x4+277x2−15876=0

Correct answer:

x1 =  9
x2 =  -9
x3 =  14
x4 =  -14

Step-by-step explanation:

y=x2  −y2+277y−15876=0 y2−277y+15876=0  a=1;b=−277;c=15876 D=b2−4ac=2772−4⋅1⋅15876=13225 D>0  y1,2​=2a−b±D​​=2277±13225​​ y1,2​=2277±115​ y1,2​=138.5±57.5 y1​=196 y2​=81   Factored form of the equation:  (y−196)(y−81)=0   x1​=+y2​​=9 x2​=−y2​​=−9 x3​=+y1​​=14 x4​=−y1​​=−14

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