Number of triangles `A B C` if `tanA=x ,tanB=x+1,a n dtanC=1-x` is ________

Answer

0

Explanation

In `Delta ABC, tan A + tan B +tan C = tan A tan B tan C`
`rArr x +x + 1 +1 -x =x (1+x) (1-x)`
or `2 + x =x -x^(3)`
or `x^(3) =-2 rArr x =-2^(1//3)`
`rArr tan A =x lt 0 rArr A` is obtuse
`rArr tanB = x + 1 =1 -2^(1//3) lt 0`
Hence, A and B are obtuse, which is not possible in a triangle.
Hence, no such triangle can exist.