Question

11. Решите уравнение.



1) (x + 3)2 - (x + 1)2 = 12
2) (x − 3)² − (x + 2)² = −25
3) (x + 2)? - (x - 1)2 = 15
4) (x - 1)2 - (x - 2)2 = 5

Answer 1

$\displaystyle\bf\\1)\\\\(x+3)^{2} -(x+1)^{2} =12\\\\x^{2} +6x+9-(x^{2} +2x+1)=12\\\\x^{2} +6x+9-x^{2} -2x-1=12\\\\4x+8=12\\\\4x=4\\\\\boxed{x=1}\\\\2)\\\\(x-3)^{2} -(x+2)^{2} =-25\\\\x^{2} -6x+9-(x^{2} +4x+4)=-25\\\\x^{2} -6x+9-x^{2} -4x-4=-25\\\\-10x+5=-25\\\\-10x=-30\\\\\boxed{x=3}\\\\3)\\\\(x+2)^{2} -(x-1)^{2} =15\\\\x^{2} +4x+4-(x^{2} -2x+1)=15\\\\x^{2} +4x+4-x^{2} +2x-1=15\\\\6x+3=15\\\\6x=12\\\\\boxed{x=2}$

$\displaystyle\bf\\4)\\\\(x-1)^{2} -(x-2)^{2} =5\\\\x^{2} -2x+1-(x^{2} -4x+4)=5\\\\x^{2} -2x+1-x^{2} +4x-4=5\\\\2x-3=5\\\\2x=8\\\\\boxed{x=4}$