Question

Number of solutions (x2-5x + 5)^x2-12x + 35= 1 of the the equation are?

Answer 1

The total number of solutions are "4".

Step-by-step explanation:

We have,

$(x^{2} -5x+5)^{x^{2} -12x+35} =1$, is only possible if

$1^{0} =1$

∴$(x^{2} -5x+5= 1$$⇒(x^{2} -5x+4) = 0$

⇒ (x - 4)(x -1) = 0

∴ x = 4 or 1

Also,

$x^{2} -12x+35=0$

⇒ $x^{2} -5x -7x+35=0$

⇒ (x - 5)(x -7) = 0

∴ x = 5 or 7

Hence, the total number of solutions are "4".