Equation `|x-3|-|x-5| = lambda` has exactly one real solution if `lambda` is equal to

If the equation |x^(2)-5x+6|-lambda x+7 lambda=0 has exactly 3 distinct solutions then lambda is equal to

If the equation |x^2-5x + 6|-lambda x+7 lambda=0 has exactly 3 distinct solutions then lambda is equal to

If the equation |x^2-5x + 6|-lambda x+7 lambda=0 has exactly 3 distinct solutions then lambda is equal to

If the equation |x^2-5x + 6|-lambda x+7 lambda=0 has exactly 3 distinct solutions then lambda is equal to

Prove that for lambda gt 1 , the equation xlog x +x =lambda has least one solution in [1 , lambda] .

Prove that for lambda gt 1 , the equation xlog x +x =lambda has least one solution in [1 , lambda] .

If the equation x^(3)-6x^(2)+9x+lambda=0 has exactly one root in (1, 3), then lambda belongs to the interval

If the equation x^(3)-6x^(2)+9x+lambda=0 has exactly one root in (1, 3), then lambda belongs to the interval

The equation x^(3)-6x^(2)+9x+lambda=0 have exactly one root in (1,3) then [lambda+1] is (where [.] denotes the greatest integer function)

If the equation 2 cos x + cos 2 lambda x=3 has only one solution , then lambda is