Question

Question :

★ The total number of integral values of ‘a’ for which the equation
➡ a² - 2a + 3 = | cos x - 2 |
have real solution for x is ? ​

Answer 1

Answer:

cos (x) -2 | lies between [1, 3]

Therefore, 1≤a2−2a+3≤3

Now Solving LHS, we get $\Rightarrow a^2 - 2a +2 \geq 0 \Rightarrow (a-1)^2 +1 \geq 0$

This is true for all "a belongs to all real number".

Solving RHS, we get a2−2a≤0abelongsto[0,2]

There fore intersection of both leads to a belonging to [0, 2] with three integer values.

ANSWER 3