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If 7, 7r , 7r^2 are the lengths of the...

If `7, 7r , 7r^2` are the lengths of the sides of a triangle, then r cannot be equal to:

A

`5/4`

B

`3/2`

C

`7/4`

D

`3/4`

Text Solution

Verified by Experts

The correct Answer is:
C
`7,7r,7r^2` : length of sides of `Delta `
(1) ` 7 + 7r gt 7r^2 , 1 + r gt r^2`
(2) ` 7 + 7r^2 gt 7r`
` 1+r^2 gt r, r in R`
(3) ` 7r + 7r^2 gt 7 , r+r^2 gt 1`
` r in ( - oo , (-1- sqrt5)/(2) ) cup ((-1 + sqrt5)/(2) , oo )`
`(1) cap (2) cap (3)`
` r in ( ( - 1 + sqrt5)/(2) , (1+ sqrt5)/(2) ) therefore r ne 7/4`
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