If a∈(0,2π ), then x2+x+x2+x tan2α is always greater than or equal to

Using A.M≥G.M we have2x2+x+x2+x tan2α ≥(x2+x.x2+x tan2α ) 1/2⇒x2+x+x2+x tan2α ≥2tanα

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Question

If $a \in (0, \frac{π}{2})$ , then $x^{2} + x + \frac{tan ^{2} α}{x ^{2} + x}$ is always greater than or equal to

2 tan α

1

2

sec^{2} α

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Elijah Discussed

a \in (0, \frac{π}{2})

, then

x^{2} + x + \frac{tan ^{2} α}{x ^{2} + x}

is always greater than or equal to

5 mins ago

Discuss this question LIVE

5 mins ago

Using

A . M \geq G . M

we have

\frac{x ^{2} + x + \frac{tan ^{2} α}{x ^{2} + x}}{2} \geq (x^{2} + x . \frac{tan ^{2} α}{x ^{2} + x})^{1/2}

\Rightarrow x^{2} + x + \frac{tan ^{2} α}{x ^{2} + x} \geq 2 tan α

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Question Text	If $a \in (0, \frac{π}{2})$ , then $x^{2} + x + \frac{tan ^{2} α}{x ^{2} + x}$ is always greater than or equal to
Answer Type	Text solution:1
Upvotes	150