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Properties of Inequalities

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Find the number of real values of x satisfying the equation 2sinx = x + (1 /x)

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Q. The number of real values of

x

satisfying the equation

\frac{| x - 5 | | x - 2 |}{| x + 9 |} = 4

t

is a real number satisfying the equation

2 t^{3} - 9 t^{2} + 30 - a = 0,

the find the value of the parameter a for which the equation

x + \frac{1}{x} = t

gives six real and distinct values of

x .

f

is an even function defined on the interval

(- 5, 5)

then find the total number of real values of

x

satisfying equation

f (x) = (\frac{x + 1}{x + 2})

Q. Find real values of

x, y, z

satisfying the equations

x + y = 2, x y - z^{2} = 1.

The set of real values of x satisfying the equation
${| x - 1 |}^{l o g_{3} (x^{2}) - 2 l o g_{x} (9)} = (x - 1)^{7}$
is

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