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В решении.
Объяснение:
При каком значении параметра a уравнение x²+ax+a-1=0 разложится как (x-7)(x+1)?
x²+ax+a-1 = (x-7)(x+1)
Раскрыть скобки:
x²+ax+a-1 = х²+х-7х-7
Привести подобные члены:
ах+а-1-х+7х+7=0
Разложить на множители:
(ах+а)-(1+х)+7(х+1)=0
а(х+1)-(1+х)+7(х+1)=0
(х+1)(а-1+7)=0
(х+1)(а+6)=0
х+1=0
х= -1;
а+6=0
а= -6.
Проверка:
Подставить вычисленное значение а в уравнение и решить его:
x²+ax+a-1=0
х²-6х-6-1=0
х²-6х-7=0
D=b²-4ac =36+28=64 √D= 8
х₁=(-b-√D)/2a
х₁=(6-8)/2
х₁= -2/2
х₁= -1;
х₂=(-b+√D)/2a
х₂=(6+8)/2
х₂=14/2
х₂=7;
ответ: х²-6х-7=(х-7)(х+1) при а= -6.
