The number of integral solution in set of x ∈(-10,10) which satisfy the inequality log (1/2)|(x)(x-3)| ≥ log 2|(x/x3-2 x2-2 x-3)|, is

Question

The number of integral solution in set of x ∈(-10,10) which satisfy the inequality log (1/2)|(x)(x-3)| ≥ log 2|(x/x3-2 x2-2 x-3)|, is (A) 9 (B) 11 (C) 13 (D) 15

Tardigrade Admin · Accepted Answer

log 2 (|( x )( x -3)|/|( x -3) x |) ≤ log 2( x 2+ x +1) ⇒ log 2 x 2 ≤ log 2( x 2+ x +1) x = -1,1,2,4,5,6,7,8,9

Q. The number of integral solution in set of $x \in (- 10, 10)$ which satisfy the inequality $lo g_{\frac{1}{2}} ∣ (x) (x - 3) ∣ \geq lo g_{2} ∣ ∣ \frac{x}{x ^{3} - 2 x ^{2} - 2 x - 3} ∣ ∣$ , is

9

11

13

15

$lo g_{2} \frac{∣ ( x ) ( x - 3 ) ∣}{∣ \frac{x - 3}{x} ∣} \leq lo g_{2} (x^{2} + x + 1)$
$\Rightarrow lo g_{2} x^{2} \leq lo g_{2} (x^{2} + x + 1)$
$x = {- 1, 1, 2, 4, 5, 6, 7, 8, 9}$

Q. The number of integral solution in set of x∈(−10,10) which satisfy the inequality log21​​∣(x)(x−3)∣≥log2​∣∣​x3−2x2−2x−3x​∣∣​, is

9

11

13

15

log2​∣xx−3​∣∣(x)(x−3)∣​≤log2​(x2+x+1) ⇒log2​x2≤log2​(x2+x+1) x={−1,1,2,4,5,6,7,8,9}

Q. The number of integral solution in set of $x \in (- 10, 10)$ which satisfy the inequality $lo g_{\frac{1}{2}} ∣ (x) (x - 3) ∣ \geq lo g_{2} ∣ ∣ \frac{x}{x ^{3} - 2 x ^{2} - 2 x - 3} ∣ ∣$ , is

$lo g_{2} \frac{∣ ( x ) ( x - 3 ) ∣}{∣ \frac{x - 3}{x} ∣} \leq lo g_{2} (x^{2} + x + 1)$
$\Rightarrow lo g_{2} x^{2} \leq lo g_{2} (x^{2} + x + 1)$
$x = {- 1, 1, 2, 4, 5, 6, 7, 8, 9}$