Question

let [x] be the greatest integer less than or equal to x, for a real number x. then the equation [x^2]=x+1 has

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Answer 1

Answer:

x+5-6+8(6)

=5x=1=9(6)

Answer 2

Given : Equation [x²] = x +1

To Find: How many solution is the given equation.

Solution:

[ x$x^{2}$] = x + 1

where , [ x$x^{2}$]--> Integer

x + 1 ---> Integer

x + 1--> should be integer

as 1 is already an integer number, that means , x is also an integer.

There value of x should be integral.

x ----> integer

==> $x^{2}$ ---> integer

then we can directly write

  $x^{2}$ = x + 1, x ∈ I

  x =( -b ± √ b² - 4ac) /2a

 x =( 1 ± √1 + 4)/2

 x =( 1 ± √5)/2 ≠ Integer

That means x has no value. Therefore, we can say that the given equation has no solution.