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Inequalities Involving Modulus Function

The set of va...

Question

The set of values of x satisfying (x2-x-1)(x2-x-7) is lesser than -5 is (a,b) union (c,d) then a+b+c+d is equal to

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\frac{3 x^{3} + 5 x - 4}{(x^{2} - 1) (x^{2} - 4)} = \frac{A}{x + 1} + \frac{B}{x - 1} + \frac{C}{x + 2} + \frac{D}{x - 2}

A + B + C + D

(x^{2} - x - 1) (x^{2} - x - 7) < - 5

The range of values of

x

satisfying the inequality is

\frac{2 x^{2} + 3 x + 4}{(x - 1) (x^{2} + 2)} = \frac{A}{x - 1} + \frac{B x + C}{x^{2} + 2}

Then the value of

B

Q. Exhaustive values of

x

satisfying the equation

| x^{4} - x^{2} - 12 | = | x^{4} - 9 | - | x^{2} + 3 |

Q. If a, b, c are distinct, then the value of x satisfying

|\begin{matrix} 0 & x^{2} - a & x^{3} - b \\ x^{2} + a & 0 & x^{2} + c \\ x^{4} + b & x - c & 0 \end{matrix}| = 0 is

(a) c
(b) a
(c) b
(d) 0

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Inequalities Involving Modulus Function

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