Вопрос школьника по предмету Алгебра
(x²-9)²-4(x²-9)+3=0
помогите решить через переменную x²-9=t с проверкой
Ответ учителя по предмету Алгебра
t²-4*t+3=0. Дискриминант D=16-4*3=4⇒t1=(4+2)/2=3, t2=(4-2)/2=1⇒х1²-9=3⇒х1²=12⇒х1=√12;х2²-9=1⇒х2²=10⇒х2=√10.
Проверка: ((√12)²-9)²-4((√12)²-9)+3=(12-9)²-4*(12-9)-3=9-4*3+3=0 — верно!
((√10)²-9)²-4((√10)²-9)+3=(10-9)²-4*(10-9)-3=1-4*1+3=0 — верно!
Ответ: х1=√12; х2=√10.
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