Given that x is a real number satisfying (5x2-26x+5/3x2-10x+3)

Question

Given that x is a real number satisfying (5x2-26x+5/3x2-10x+3) < 0 , then (A) x <(1/5) (B) (1/5) < x < 3 (C) x > 5 (D) (1/5) < x < (1/3) or 3 < x < 5

Tardigrade Admin · Accepted Answer

We have, (5 x2-26 x+5/3 x2-10 x+3)<0 ⇒ (5 x2-25 x-x+5/3 x2-9 x-x+3)<0 ⇒ (5 x(x-5)-1(x-5)/3 x(x-3)-1(x-3))<0 ⇒ ((x-5)(5 x-1)/(x-3)(3 x-1))< 0 ∴ x ∈((1/5), (1/3)) ∪(3,5)

Q. Given that $x$ is a real number satisfying $\frac{5 x ^{2} - 26 x + 5}{3 x ^{2} - 10 x + 3} < 0,$ then

$x < \frac{1}{5}$

$\frac{1}{5} < x < 3$

$x > 5$

$\frac{1}{5} < x < \frac{1}{3}$ or $3 < x < 5$

Q. Given that x is a real number satisfying 3x2−10x+35x2−26x+5​<0, then

x<51​

51​<x<3

x>5

51​<x<31​ or 3<x<5

We have, 3x2−10x+35x2−26x+5​<0 ⇒3x2−9x−x+35x2−25x−x+5​<0 ⇒3x(x−3)−1(x−3)5x(x−5)−1(x−5)​<0 ⇒(x−3)(3x−1)(x−5)(5x−1)​<0 ∴x∈(51​,31​)∪(3,5)

Q. Given that $x$ is a real number satisfying $\frac{5 x ^{2} - 26 x + 5}{3 x ^{2} - 10 x + 3} < 0,$ then

$x < \frac{1}{5}$

$\frac{1}{5} < x < 3$

$x > 5$

$\frac{1}{5} < x < \frac{1}{3}$ or $3 < x < 5$