Three distinct real numbers- a - b - c are in G-P- such that a - b - c - x b- thenA- -1- x -2B- -1- x -3C- 0- x -1D- x3

The correct option is D x lt; 1 or x gt;3 a + ar + ar^2 = x. ar or, r^2 + r (1 x) + 1 = 0, r is real ∆ gt;0 i.e.(1 x)^2 4 gt;0 Or,x^2 2x 3 gt;0 Or ...

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Standard XI

Mathematics

Properties of Argument

Three distinc...

Question

Three distinct real numbers, a, b, c are in G.P. such that a + b+ c= x b, then

0<x<1

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-1<x<3

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x<-1 or x>3

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-1<x<2

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Solution

The correct option is C
x<-1 or x>3

a + ar + a $r^{2}$ = x. ar

or, $r^{2}$ + r (1-x) + 1 = 0, r is real

∆>0 i.e. ${(1 - x)}^{2}$ - 4 >0

Or, $x^{2}$ -2x-3>0

Or, (x+1) (x-3)>0

⇒ x<-1 or x>3

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Three distinct real numbers, a, b, c are in G.P. such that a + b+ c= x b, then

The correct option is C x<-1 or x>3 a + ar + ar2 = x. ar or, r2 + r (1-x) + 1 = 0, r is real ∆>0 i.e.(1−x)2- 4 >0 Or,x2-2x-3>0 Or, (x+1) (x-3)>0 ⇒ x<-1 or x>3

The correct option is C
x<-1 or x>3

a + ar + a $r^{2}$ = x. ar

or, $r^{2}$ + r (1-x) + 1 = 0, r is real

∆>0 i.e. ${(1 - x)}^{2}$ - 4 >0

Or, $x^{2}$ -2x-3>0

Or, (x+1) (x-3)>0

⇒ x<-1 or x>3