Question

Find the number of solutions of x^2-12x+35=[x]+[-x]​

Answer 1

Answer:

Plz follow me

Mark as brainliest

The number of solutions is 2 because it is a quadratic equation

Answer 2

Therefore the given equation x² - 12x + 35 = [x] + [-x] has '4' solutions.

Given:

The equation: x² - 12x + 35 = [x] + [-x]

To Find:

The number of  solutions of the given equation, x² - 12x + 35 = [x] + [-x]

Solution:

The given question can be solved as shown below.

Given equation: x² - 12x + 35 = [x] + [-x]

[x] - Step function which has lower floor value that is if x=5.5 the [x] = 5

Now coming to the question,

If x is an integer, then [x] = x

⇒ x² - 12x + 35 = x-x = 0

⇒ x² - 12x + 35 = 0

⇒ x² - 5x - 7x + 35 = 0

⇒ x( x-5 ) + 7(x - 5 )  =0

⇒ x = -7 or 5

Hence 2 solutions if x is a step function,

If x is a decimal number, [x.y] = x and [-x.y] = -x-1

⇒ x² - 12x + 35 = x - ( -x - 1 )

⇒ x² - 12x + 35 = x + x + 1

⇒ x² - 12x + 35 = 2x + 1

⇒ x² - 10x + 34 = 0

Hence this equation also has 2 equations,

So totally the given equation x² - 12x + 35 = [x] + [-x] has '4' solutions.

Therefore the given equation x² - 12x + 35 = [x] + [-x] has '4' solutions.

#SPJ2