If a - b - c - 3- then find the value of 1-1 - a-1 - b- - 1-1 - b-1 - c- - 1-1 - c-1 - a- - Maths Q - A

Find the required value:Given: a+b+c = 3……………( 1)1/(1 a)(1 b)+1/(1 b)(1 c)+1/(1 c)(1 a)Taking LCM := (1 c)+(1 a)+(1 b)/(1 a)(1 b)(1 c)0ex0ex= 3 (a+ ...

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Standard VI

Mathematics

Ladder Diagram

If a + b + c ...

Question

If $a + b + c = 3$ , then find the value of $\frac{1}{(1 - a) (1 - b)} + \frac{1}{(1 - b) (1 - c)} + \frac{1}{(1 - c) (1 - a)}$ .

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Solution

Find the required value:
Given: $a + b + c = 3$ ……………( $1$ )
$\frac{1}{(1 - a) (1 - b)} + \frac{1}{(1 - b) (1 - c)} + \frac{1}{(1 - c) (1 - a)}$
Taking LCM :
$= \frac{(1 - c) + (1 - a) + (1 - b)}{(1 - a) (1 - b) (1 - c)} = \frac{3 - (a + b + c)}{(1 - a) (1 - b) (1 - c)}$
From equation $1$ we have $a + b + c = 3$ So
$= \frac{3 - 3}{(1 - a) (1 - b) (1 - c)} = 0$
Hence the value of $\frac{1}{(1 - a) (1 - b)} + \frac{1}{(1 - b) (1 - c)} + \frac{1}{(1 - c) (1 - a)}$ is $0$ .

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If a+b+c=3, then find the value of 1(1-a)(1-b)+1(1-b)(1-c)+1(1-c)(1-a).

Find the required value:Given: a+b+c=3……………( 1)1(1-a)(1-b)+1(1-b)(1-c)+1(1-c)(1-a)Taking LCM :=(1-c)+(1-a)+(1-b)(1-a)(1-b)(1-c)=3-(a+b+c)(1-a)(1-b)(1-c)From equation 1 we have a+b+c=3So=3-3(1-a)(1-b)(1-c)=0Hence the value of 1(1-a)(1-b)+1(1-b)(1-c)+1(1-c)(1-a) is 0.

If $a + b + c = 3$ , then find the value of $\frac{1}{(1 - a) (1 - b)} + \frac{1}{(1 - b) (1 - c)} + \frac{1}{(1 - c) (1 - a)}$ .