Question

Задание в прикрепленном фото

Answer 1

$2)\\\\x^2-x(\sqrt6-1)-\sqrt6=0\\D=(\sqrt6-1)^2+4\sqrt6=6-2\sqrt6+1+4\sqrt6=6+2\sqrt6+1=(\sqrt6+1)^2\\x_{1,2}=\frac{\sqrt6-1^+_-(\sqrt6+1)}{2}\\x_1=-1 ; x_2=\sqrt6\\Ans: -1; \sqrt6\\----------\\3)\\\\\frac{2(x^2-9)}{5}-\frac{x+1}{2}=\frac{x-41}{4} |*40\\16(x^2-9)-20(x+1)=10(x-41)\\16x^2-144-20x-20=10x-410\\16x^2-30x+246=0 | \div2\\8x^2-15x+123=0\\D=225-8*4*123<0\\x \notin \mathbb{R}\\Ans: x \notin \mathbb{R}\\\\----------$

$4)\\\\\frac{x^2+5x}{3}-\frac{x+2}{2}=\frac{2x^2-2}{8} |*24\\8(x^2+5x)-12(x+3)=3(2x^2-2)\\8x^2+40x-12x-36=6x^2-6\\2x^2+28x-30=0 |\div 2\\x^2+14x-15=0 \\x_1=-15; x_2=1\\Ans: -15; 1$