Question

FIND OUT THE NUMBER OF VALUES OF X SATISFYING GIVEN EQUATION.. solve it PLZZ... I NEED PROPER EXPLANATION..​

Answer 1

Answer:

RHS is 1

now LHS can be equal to 1 under two possibilities only

possibility 1:

If |x-3| = 1, the value of whole expression will be 1

now

|x - 3| = 1 gives two solution

x - 3 = 1, x = 4 or

-x+3 = 1, x = 2

possibility 2

If exponent 3x^2 - 10x +3 is equal to zero, value of whole expression will be 1 as a^0 is 1. however, in this case, base should not be equal to zero i.e. x cannot be 3.

now

3x^2 - 10x + 3 = 0

3x^2 - 9x - x + 3 = 0

3x(x-3) - 1(x-3) = 0

(x-3)(3x-1) = 0

this gives

x = 3 and 1/3

but as discussed above, x= 3 will make expression of the form 0^0 which is not defined. so x= 3 is not our solution.

so the possible solutions are

x= 1/3, 2, 4