If a- b- c are in arithmetic progression- then 1-a-b- 1-a-c- 1-b-c- are in

The correct option is A AP.1/√(a) + √(b),1/√(a) + √(c),1/√(b) + √(c)are in AP, if 1/√(a) + √(c) 1/√(a) + √(b)=1/√(b) + √(c) 1/√(a) + √(c) Ie, if √(b) √(c)/√( ...

You visited us 2 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Logarithmic Inequalities

If a, b, c ar...

Question

If a, b, c are in arithmetic progression, then $\frac{1}{\sqrt{a} + \sqrt{b}}, \frac{1}{\sqrt{a} + \sqrt{c}}, \frac{1}{\sqrt{b} + \sqrt{c}},$ are in

AP.

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

GP.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

HP.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A AP.
$\frac{1}{\sqrt{a} + \sqrt{b}}, \frac{1}{\sqrt{a} + \sqrt{c}}, \frac{1}{\sqrt{b} + \sqrt{c}} a r e i n A P, i f \frac{1}{\sqrt{a} + \sqrt{c}} - \frac{1}{\sqrt{a} + \sqrt{b}} = \frac{1}{\sqrt{b} + \sqrt{c}} - \frac{1}{\sqrt{a} + \sqrt{c}} I e, i f \frac{\sqrt{b} - \sqrt{c}}{\sqrt{a} + \sqrt{b}} = \frac{\sqrt{a} - \sqrt{b}}{\sqrt{b} + \sqrt{c}} I e . i f b - c = a - b, w h i c h i s t r u e$

Suggest Corrections

Similar questions

If a,b,c are in arithmetic progression , then show that the following are in arithematic progression :-

1. b+c , c+a , a+b

2. a+3k , b+3k , c+3k

3. a\7k , b\7k , c\7k

4. b+c-a , c+a-b , a+b-c

Q. If

a^{2}, b^{2}, c^{2}

are in arithmetic progression, then the terms

\frac{1}{(a + b)},

\frac{1}{(c + a)}, \frac{1}{(b + c)}

will form

Let a, b, c are non-zero real numbers such that \frac{1}{a}, \frac{1}{b}, \frac{1}{c} are in arithmetic progression and a, b, -2c are in geometric progression, then which of the following statement(s) must be true?

If $a, \frac{1}{b}, c$ and $\frac{1}{p}, q, \frac{1}{r}$ form two arithmetic progression of the same common difference, then a, q, c are in A.P. if

Q. If a, b, c and d are in harmonic progression, then

\frac{1}{a}

\frac{1}{b}

\frac{1}{c}

and

\frac{1}{d}

, are in ______ progression.

Join BYJU'S Learning Program

If a, b, c are in arithmetic progression, then 1√a+√b,1√a+√c,1√b+√c, are in

The correct option is A AP.1√a+√b,1√a+√c,1√b+√care in AP, if1√a+√c−1√a+√b=1√b+√c−1√a+√cIe,if√b−√c√a+√b=√a−√b√b+√cIe.if b−c=a−b,which is true

If a, b, c are in arithmetic progression, then $\frac{1}{\sqrt{a} + \sqrt{b}}, \frac{1}{\sqrt{a} + \sqrt{c}}, \frac{1}{\sqrt{b} + \sqrt{c}},$ are in