Вопрос школьника по предмету Математика
Решите уравнение (3х-4а)2(вторая степень)=(х+2а)2(вторая степень)
Ответ учителя по предмету Математика
Ответ:
(3x-4a)^2=(x+2a)^2
(3x)^2-3x*4a*2+(4a)^2=x^2+2*x*2a+(2a)^2
9x^2-24ax+16a^2=x^2+4ax+4a^2
переносим все в левую часть:
9x^2-24ax+16a^2-x^2-4ax-4a^2=0
9x^2-x^2-24ax-4ax+16a^2-4a^2=0
8x^2-28ax+12a^2=0 |/4
2x^2-7ax+3a^2=0
D=(-7)^2-4*3*2=49-24=25
x1=(7+5)/4=3
x2=(7-5)/4=2/4=1/2
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