Question

решите уравнение пожалуйста​

Answer 1

Ответ:

$x=2$

Пошаговое объяснение:

1. $\sqrt{x+2}-\sqrt{2x-3} =1$

2. $\sqrt{x+2} =1+\sqrt{2x-3}$

3. $x+2=1+2\sqrt{2x-3} +2x-3$

4. $x+2=-2+2\sqrt{2x-3}+2x$

5. $-2\sqrt{2x-3}=-2+2x-x-2$

6. $-2\sqrt{2x-3}=-4+x$

7. $4(2x-3)=x^{2}-8x+16$

8. $8x-12=x^{2}-8x+16$

9. $8x-12-x^{2}+8x-16=0$

10. $16x-28-x^{2}=0$

11. $-x^{2}+16x-28=0$

12. $x^{2}-16x+28=0$

13. $x^{2}-2x-14x+28=0$

14. $x*(x-2)-14(x-2)=0$

15. $(x-2)*(x-14)=0$

16. $\left \{ {{x-2=0} \atop {x-14=0}} \right.$

17. $\left \{ {{x=2} \atop {x=14}} \right.$

18.$\left \{ {{\sqrt{2+2}-\sqrt{2*2-3}=1 } \atop {\sqrt{14+2}-\sqrt{2*14-3}=1 }} \right.$

19. $\left \{ {{1=1} \atop {-1=1}} \right.$

20. $\left \{ {{x=2} \atop {x\neq 14}} \right.$

21. $x=2$