Number of triangles ABC if tan A = x, tan B = x + 1,and tan C = 1- x is_____.

△ABC,tan ⁡A+tan ⁡B+tan ⁡C=tan⁡ A tan⁡ B tan ⁡C⇒ x+x+1+1−x=x(1+x)(1−x)or  2+x=x−x3or  x3=−2⇒x=−21/3⇒tan⁡A=x<0 ⇒A is obtuse ⇒tan⁡B=x+1=1−21/3<0Hence, A and B are obtuse, which is not possible in a triangle.Hence, no such triangle can exist.