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Бантик1999
@Бантик1999
November 2021
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x^3+5x^2-4x-20/x^2+3x-10 сократить дробь
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Разложим на множители числитель и знаменатель
x^3 + 5x^2 - 4x - 20 = 0;
x^2(x+5)- 4(x+5) =0;
(x+5)(x^2 -4) = 0;
(x+5)(x-2)(x+2) = 0;
⇒x^3 + 5x^2 - 4x - 20 = (x+5)(x-2)(x+2);
x^2 + 3x - 10 = 0;
D= 9 +40 = 49= 7^2;
x1 = - 5;
x 2 = 2;
⇒x^2 + 3x - 10 = (x+5)(x-2);
Упростим выражение:
(x^3+ 5x^2 - 4x - 20) / (x^2 + 3x - 10) =
=(x+5)(x+2)(x-2) / (X=5)(x-2) = x + 2
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Answers & Comments
x^3 + 5x^2 - 4x - 20 = 0;
x^2(x+5)- 4(x+5) =0;
(x+5)(x^2 -4) = 0;
(x+5)(x-2)(x+2) = 0;
⇒x^3 + 5x^2 - 4x - 20 = (x+5)(x-2)(x+2);
x^2 + 3x - 10 = 0;
D= 9 +40 = 49= 7^2;
x1 = - 5;
x 2 = 2;
⇒x^2 + 3x - 10 = (x+5)(x-2);
Упростим выражение:
(x^3+ 5x^2 - 4x - 20) / (x^2 + 3x - 10) =
=(x+5)(x+2)(x-2) / (X=5)(x-2) = x + 2