Prove that for real values of `x ,(a x^2+3x-4)//(3x-4x^2+a)` may have any value provided a lies between 1 and 7.

Prove that for real values of x,(ax^(2)+3x-4)/(3x-4x^(2)+a) may have any value provided a lies between 1 and 7.

Show that for all real values of x the value of (x^2-3x+4)/(x^2+3x+4) always lie between 1/7 and 7.

Prove that if x=(7+4sqrt(3) then value of x^(2)+(1)/(x^(2)) is 194

Prove that (6x^(2)-22x+21)/(5x^(2)-18x +17) for real values of x lies between 1 and (5)/(4) .

If the equation y^2+x^2-10x+21=0 is satisfied by real values of x and y, prove that x lies between 3 and 7 and y lies between (-2) and 2.

If x is real,prove that ((x-2)(x-4))/((x-1)(x-3)) can have any real value.

If x is real,prove that ((x-2)(x-4))/((x-1)(x-3)) can have any real value.

IF x is real then the value of ( x ^2 - 3x +4)/( x^2 +3x +4) lies in the interval