Question

The inequality $(2n+7)<(n+3{)}^2$ is true for

• A. All negative numbers.
• B. All whole numbers
• C. All natural numbers
• D. None of these

Answer 1

Answer: (D)

None of these

Given inequality,

$(2n+7)<(n+3{)}^2$

using,

$(a+b{)}^2=a^2+b^2+2ab$

$(2n+7)<n^2+9+6n$

$0<n^2+4n+2$

$n^2+4n+2>0$

using number line

$n\in (-\infty ,-2-\sqrt{2})\cup (-2+\sqrt{2},\infty )$

so, option D is correct.