If a-bx a-bx - b-cx b-cx - c-dx c-dx x- 0 - then show that a-b-c and d are in G-P-

Given, a+bxa bx=b+cxb cx=c+dxc dx applying componendo and dividendo, a+bx+a bxa+bx (a bx)=b+cx+b cxb+cx (b cx)=c+dx+c dxc+dx (c dx) 2a+02bx+0=2b+02 ...

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Byju's Answer

Standard XII

Mathematics

Continuity of a Function

If a+bx a-b...

Question

If $\frac{a + b x}{a - b x} = \frac{b + c x}{b - c x} = \frac{c + d x}{c - d x} (x \neq 0)$ , then show that $a, b, c$ and $d$ are in $G . P .$

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Solution

Given,

$\frac{a + b x}{a - b x} = \frac{b + c x}{b - c x} = \frac{c + d x}{c - d x}$

applying componendo and dividendo,

$\frac{a + b x + a - b x}{a + b x - (a - b x)} = \frac{b + c x + b - c x}{b + c x - (b - c x)} = \frac{c + d x + c - d x}{c + d x - (c - d x)}$

$\frac{2 a + 0}{2 b x + 0} = \frac{2 b + 0}{2 c x + 0} = \frac{2 c + 0}{2 d x + 0}$

$\frac{a}{b x} = \frac{b}{c x} = \frac{c}{d x}$

$\frac{a}{b} = \frac{b}{c} = \frac{c}{d}$

$\frac{b}{a} = \frac{c}{b} = \frac{d}{c}$

Therefore a,b,c,d are in G.P.

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Similar questions

If $\frac{a + b x}{a - b x} = \frac{b + c x}{b - c x} = \frac{c + d x}{c - d x} (x \neq 0),$ then show that a, b, c and d are in G.P.

If $\frac{a + b x}{a - b x} = \frac{b + c x}{b - c x} = \frac{c + d x}{c - d x} (x \neq 0)$ , then show that a, b, c and d are in G.P.

\frac{a + b x}{a - b x} = \frac{b + c x}{b - c x} = \frac{c + d x}{c - d x}, (x \neq 0)

then show that

a, b, c

and

d

are in G.P.

Q. If

\frac{a + b x}{a - b x} = \frac{b + c x}{b - c x} = \frac{c + d x}{c - d x} (x \neq 0)

, then show that

a, b, c

and

d

are in G.P

Q. If

\frac{a + b x}{a - b x} = \frac{b + c x}{b - c x} = \frac{c + d x}{c - d x}

(x ≠ 0), then show that a, b, c and d are in G.P.

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If a+bxa−bx=b+cxb−cx=c+dxc−dx(x≠0), then show that a,b,c and d are in G.P.

Given,a+bxa−bx=b+cxb−cx=c+dxc−dxapplying componendo and dividendo,a+bx+a−bxa+bx−(a−bx)=b+cx+b−cxb+cx−(b−cx)=c+dx+c−dxc+dx−(c−dx)2a+02bx+0=2b+02cx+0=2c+02dx+0abx=bcx=cdxab=bc=cdba=cb=dcTherefore a,b,c,d are in G.P.

If $\frac{a + b x}{a - b x} = \frac{b + c x}{b - c x} = \frac{c + d x}{c - d x} (x \neq 0)$ , then show that $a, b, c$ and $d$ are in $G . P .$