Question

What is the smallest integer that satisfies the inequality (x−3)/(x2−8x−20)>0

explain with steps pls


A. 10

B. 3

C. 0

D. -1

E. -2

Answer 1

Given Question :-

• What is the smallest integer that satisfies the inequality (x−3)/(x^2−8x−20)>0

• A. 10

• B. 3

• C. 0

• D. -1

• E. - 2

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$\large\underline\purple{\bold{Solution :- }}$

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$\bf \:  ⟼ Consider \: \dfrac{x - 3}{ {x}^{2} - 8x - 20 } > 0$

$\sf \:  ⟼\dfrac{x - 3}{ {x}^{2} - 10x + 2x- 20 } > 0$

$\sf \:  ⟼ \: \dfrac{x - 3}{x(x - 10) + 2(x - 10)} > 0$

$\sf \:  ⟼ \: \dfrac{x - 3}{(x - 10)(x + 2)} > 0$

$\sf \:  ⟼ \: \dfrac{(x - 3)(x + 2)(x - 10)}{ {(x - 10)}^{2} {(x + 2)}^{2} } > 0$

$\sf \:  ⟼ \: x \: \epsilon \: ( - 2, \: 3) \: \cup \: (10 \: , \infty \: )$

☆ So, smallest integer satisfy the inequality is x = - 1.

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$\large{\boxed{\boxed{\bf{Hence, \: option \: ( d) \: is \: correct}}}}$

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