If a - b - ab - and a - H 1- H 2-b form H-P-then 1- H 1-1- H 2 equals toD -2-

The correct option is A 1/a,1/H_1,1/H_2,1/b are in A.P Let the common difference be d. 1/H_1 = 1/a + d 1/H_2 = 1/a + 2d 1/b = 1/a + 3d 1/H_1 + 1/H_1 = (1/a ...

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Byju's Answer

Standard XI

Mathematics

Non Removable Discontinuities

If a + b =α, ...

Question

If a+b = $α$ ,ab = $β$ ,and a, $H_{1}$ , $H_{2}$ ,b form H.P,then $\frac{1}{H_{1}}$ + $\frac{1}{H_{2}}$ equals to

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Solution

The correct option is A

$\frac{1}{a}, \frac{1}{H_{1}}, \frac{1}{H_{2}}, \frac{1}{b}$ are in A.P

Let the common difference be d.

$\frac{1}{H_{1}}$ = $\frac{1}{a}$ + d

$\frac{1}{H_{2}}$ = $\frac{1}{a}$ + 2d

$\frac{1}{b}$ = $\frac{1}{a}$ + 3d

$\frac{1}{H_{1}}$ + $\frac{1}{H_{1}}$ = ( $\frac{1}{a}$ + d ) + ( $\frac{1}{a}$ + 2d )

= $\frac{1}{a}$ + ( $\frac{1}{a}$ + 3d)

= $\frac{1}{a}$ + $\frac{1}{b}$

= $\frac{a + b}{a b}$ = $\frac{α}{β}$

Or

$\frac{1}{b}$ - $\frac{1}{H_{1}}$ = $\frac{1}{H_{2}}$ - $\frac{1}{b}$

$\Rightarrow$ $\frac{1}{H_{1}}$ + $\frac{1}{H_{2}}$ = $\frac{1}{a}$ + $\frac{1}{b}$

= $\frac{a + b}{a b}$

= $\frac{α}{β}$

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If a+b = α,ab = β,and a,H1,H2,b form H.P,then 1H1 + 1H2 equals to

The correct option is A 1a,1H1,1H2,1b are in A.P Let the common difference be d. 1H1 = 1a + d 1H2 = 1a + 2d 1b = 1a + 3d 1H1 + 1H1 = (1a + d ) + (1a + 2d ) = 1a + (1a + 3d) = 1a + 1b = a+bab = αβ Or 1b - 1H1 = 1H2 - 1b ⇒ 1H1 + 1H2 = 1a + 1b = a+bab = αβ

If a+b = $α$ ,ab = $β$ ,and a, $H_{1}$ , $H_{2}$ ,b form H.P,then $\frac{1}{H_{1}}$ + $\frac{1}{H_{2}}$ equals to