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dimanglush
@dimanglush
July 2022
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1) разложить на множители: x^4+3x^2-4= 2) выделить полный квадрат: 2x^2+7x+5= ?
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uekmyfhfp
1) x^4 + 3x^2 - 4 = 0;
x^2 = t;
t^2 + 3t - 4 = 0;
D = 9 + 16 = 25 = 5^2;
t1 = 1;
t2 = - 4;
(t-1)(t+4) = 0;
(x^4 + 3x^2 - 4) = (x^2 - 1) (x^2 + 4) =(x-1)(x+1)(x^2 + 4) .
2) 2x^2 + 7x + 5= 2(x^2 + 3,5 x + 2,5) = 2(x^2 + 2*1,75*x + 1,75^2 -1,75^2 + 2,5) =
=2((x+1,75)^2 - 0,5625)= 2(x+1,75)^2 - 1,125
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Answers & Comments
x^2 = t;
t^2 + 3t - 4 = 0;
D = 9 + 16 = 25 = 5^2;
t1 = 1;
t2 = - 4;
(t-1)(t+4) = 0;
(x^4 + 3x^2 - 4) = (x^2 - 1) (x^2 + 4) =(x-1)(x+1)(x^2 + 4) .
2) 2x^2 + 7x + 5= 2(x^2 + 3,5 x + 2,5) = 2(x^2 + 2*1,75*x + 1,75^2 -1,75^2 + 2,5) =
=2((x+1,75)^2 - 0,5625)= 2(x+1,75)^2 - 1,125