Найдите корень уравнения:
а) 5 + х² = (х + 1)(x + 6);
б) 2х(х - 8) = (х + 1)(2x - 3);
в) (3x - 2)(х + 4) - 3(х + 5)(х - 1) = 0;
г) х² + х(6 - 2х) = (х- 1)(2 - х) - 2.

Решение:


а) 5 + х² = (х + 1)(x + 6) => 5 + х² = х² + 6x + x + 6 => 7x = -1 => x = -1/7;
б) 2х • (х - 8) = (х + 1)(2x - 3) => 2х² - 16х = 2х² - Зх + 2х - 3 => 15х = 3 => х = 0,2;
в) (3x - 2)(х + 4) - 3 • (х + 5)(х - 1) = 0 => 3х² + 12x - 2х - 8 - 3х² + 3х - 15х + 15 = 0 => 10x - 12x = 8 - 15 => -2х =
= -7 => х = 3,5;
г) х² + х • (6 - 2х) = (х - 1)(2 - х) - 2 => х² + 6х - 2х2 = 2х - х² - 2 + х - 2 => 6х - 2х - х = -4 => Зx = -4 => х = -1 1/3.