Помогите решить первые три задания!Алгебра,10 класс

Question

Алгебра

Vazhavekk

6 год назад

Помогите решить первые три задания!Алгебра,10 класс

ОТВЕТЫ

Svishhov

Aug 15, 2019

а)
( $(\sqrt{1} -x)^{2} =(x+1)^{2} amp;#10;amp;#10;x+1 \geq 0 ; x \geq -1amp;#10;amp;#10;1-x=x^{2} +2x+1amp;#10;amp;#10; x^{2} +3x=0amp;#10;amp;#10;x(x+3)=0amp;#10;amp;#10;x1=0amp;#10;amp;#10;x2=-3$

Ответ: х=0
б)
$\sqrt{x+7} + \sqrt{x-2} =9amp;#10;amp;#10; \sqrt{x+7} =9- \sqrt{x-2}amp;#10;amp;#10;x+7=(9- \sqrt{x-2})amp;#10;amp;#10;x+7=81-18 \sqrt{x-2} +x-2amp;#10;amp;#10;18 \sqrt{x-2} =81+x-2-x-7amp;#10;amp;#10;18 \sqrt{x-2} =72 amp;#10;amp;#10; \sqrt{x-2} 4amp;#10;amp;#10;x-2=16amp;#10;amp;#10;x=18$

в)
$(1-2x)-2 \sqrt{((1-2x)(13+x)} + (13+x)=x+4amp;#10;amp;#10;2 \sqrt{((1-2x)(13+x))} =1-2x+13x-x-4amp;#10;amp;#10; \sqrt{((1-2x)(13+x))} =5-xamp;#10;amp;#10;(1-2x)(13-x)=25-10x+ x^{2} amp;#10;amp;#10;13-25x- 2x^{2} =25-10x+ x^{2} amp;#10;amp;#10; 3x^{2} +15x+12=0amp;#10;amp;#10; x^{2} +5x+4=0amp;#10;amp;#10;x1,2=(-5+\- \sqrt{(25-16)} ) : 2 = (-5+\-3) : 2amp;#10;amp;#10;x1=-4 ; x2=-1amp;#10;amp;#10;x=-4$

30