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If the sides of triangle `ABC` are in G.P with common ratio `r (r |
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Answer» it is given that a,b,c are in GP a=1, b=r, c=`r^2` sum of two sides is always greater than the third side (a+b)>c (1+r)>`r^2` `r^2-r-1<0` r=`(1+-sqrt(1+4))/2` r=`(1+-sqrt(5))/2` `(r-(1+sqrt5/2))(r-(1-sqrt5/2))`<0 let r=0 `((1+sqrt5)(1-sqrt5))/2` `(1^2-5)/2=-4/2=-2<0` `r in ((1-sqrt5)/2,(1+sqrt5)/2))` so, `r<1/2 (1+sqrt5)` |
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