Grade 11Algebra

If 1/a+1/a-b+1/c+1/c-b =0 and a+c-b not equal to 0 then prove a,b,c are in hp

Harshidaa S Nair

8 Years agoGrade 11

1 Answer

Ritesh Khatri

8 Years ago

After rearranging we get

$\Rightarrow \frac{1}{a}+\frac{1}{c-b}+\frac{1}{a-b}+\frac{1}{c}=0$

After taking LCM of first two and last to terms we get

$\Rightarrow \frac{c-b+a}{a(c-b)}+\frac{c+a-b}{c(a-b)}=0$

since a+c-b is not equal to 0

therefore $\frac{1}{a(c-b)}+\frac{1}{c(a-b)}=0$

Taking LCM

$\Rightarrow \frac{ac-bc+ac-ab}{ac(c-b)(a-b)}=0$

Therefore numerator is equal to zero

$\Rightarrow \ ac-bc+ac-ab = 0$

$\Rightarrow \ 2ac = bc+ab$

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

Which is necessory condition to proove that a, b and c are in HP

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If 1/a+1/a-b+1/c+1/c-b =0 and a+c-b not equal to 0 then prove a,b,c are in hp

Harshidaa S Nair

1 Answer

Ritesh Khatri

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