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The set of all real numbers a such that ...

The set of all real numbers `a` such that `a^2+2a ,2a+3,a n da^2+3a+8` are the sides of a triangle is_____

Text Solution

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The correct Answer is:
`a gt 5`
Since `a^(2)+2a, 2a+3 and a^(2)+3a+8` from sides of a triangle
Now, `a^(2)+3a+8lt(a^(2)+2a)+(2a+3)`
`rArr a^(2)3a+8lta^(2)+4a+3`
`rArr alt5 " "...(i)`
Also, `(a^(2)+3a+8)+(2a+3)gta^(2)+2a`
`rArr 3agt-11`
`rArr agt-(11)/(3)" "...(ii)`
Again `(a^(2)+3a+8)+(a^(2)+2a)gt2a+3`
`rArr 2a^(2)+3a+5gt0`
whihc is always ture
`:.` Triangle is formed if `agt5`
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