Question

решите уравнение

 

$sqrt{x+5}+sqrt{5-x}=4$

Answer 1

$sqrt{x+5}+sqrt{5-x}=4\ sqrt{x+5}=4-sqrt{5-x}\ x+5=16-8sqrt{5-x}+5-x\ 8sqrt{5-x}=16-2x\4sqrt{5-x}=8-x\ 16(5-x)=64-16x+x^2\ 80-16x=64-16x+x^2\ x^2=16\ x_1=4\x_2=-4$

x+5>=0    и 5-x>=0

x>=-5   и x<5

Ответ: -4; 4

Answer 2

$\sqrt{x+5}+sqrt{5-x}=4\ D_f:x+5geq0 wedge 5-xgeq0\ D_f:xgeq-5 wedge xleq5\ D_f:xinlangle-5,5rangle\ sqrt{x+5}=4-sqrt{5-x}\ x+5=(4-sqrt{5-x})^2\ x+5=16-8sqrt{5-x}+5-x\ 8sqrt{5-x}=-2x+16\ 4sqrt{5-x}=-x+8\ 16(5-x)=(-x+8)^2\ 80-16x=x^2-16x+64\ x^2=16\ x=-4 vee x=4$