Question

1. Решите уравнение:
а) х2 + (х – 2)(х + 5) = - 1; б) (х – 3)2 + 4(х – 5) = 4.

Answer 1

а) 1,5 и -3;

б) 2 и -3.

Объяснение:

$a) x^{2} +(x-2)(x+5)=-1\\x^{2} +x^{2} +5x-2x-10=-1\\2x^{2} +3x-9=0\\D=9+72=81\\x_{1} =\frac{-3+9}{4} =1,5, \\x_{2} =\frac{-3-9}{4} =-3 \\\\\\b) (x-3)^{2}+4(x-5)=4\\x^{2} -6x+9+4x-20-4=0\\x^{2} -2x-15=0\\x_{1} x_{2} =-15,\\x_{1} + x_{2} =2,\\x_{1}=5, x_{2}=-3.\\$