Question

Номер 143, 4 и 5 пункты

Answer 1

$4)\\2x^2+3x+3-5\sqrt{2x^2+3x+9}=0\\2x^2+3x+9-5\sqrt{2x^2+3x+9}-6=0\\\\\sqrt{2x^2+3x+9}=k\geq 0\\\\k^2-5k-6=0\\k_1=6 ; k_2=-1\\\\\sqrt{2x^2+3x+9}=6\\2x^2+3x+9-36=0\\2x^2+3x-27=0\\x_1=-\frac{9}{2} ; x_2=3\\\\\sqrt{2x^2+3x+9}=-1\\x \notin \mathbb{R}\\\\Ans: x=-\frac{9}{2} ; x=3$

$5)\\5x^2-20x+6-2\sqrt{x^2-4x+9}=0\\5x^2-20x+45-2\sqrt{x^2-4x+9}-39=0\\5(x^2-4x+9)-2\sqrt{x^2-4x+9}-39=0\\\\\sqrt{x^2-4x+9}=k \geq 0\\\\5k^2-2k-39=0\\k_1=3 ; k_2=-\frac{13}{5}\\\\\sqrt{x^2-4x+9}=3\\x^2-4x+9=9\\x^2-4x=0\\x(x-4)=0\\x_1=0 ; x_2=4\\\\\sqrt{x^2-4x+9}=-\frac{13}{5}\\x \notin \mathbb{R}\\\\Ans: x=0 ; x=4$