If a + b + c + d = 4 then the value of [1/(1 – a)(1 – b)(1 – c)] + [1/(1 – b)(1 – c)(1 – d)] + [1/(1 – c)(1 – d)(1 – a)] + [1/(1 – d)(1 – a)(1 – b)]:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 0
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Application |
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Given: a + b + c + d = 4 [1/(1 – a)(1 – b)(1 – c)] + [1/(1 – b)(1 – c)(1 – d)] + [1/(1 – c)(1 – d)(1 – a)] + [1/(1 – d)(1 – a)(1 – b)] ⇒ [(1 – d)/(1 – a)(1 – b)(1 – c)(1 – d)] + [(1 – a)/(1 – a)(1 – b)(1 – c)(1 – d)] + [(1 – b)/(1 – c)(1 – d)(1 – a)(1 – b)] + [(1 – c)/(1 – d)(1 – c)(1 – a)(1 – b)] ⇒ [(1 – a + 1 – b + 1 – c + 1 – d)/(1 – a)(1 – b)(1 – c)(1 – d)] ⇒ [(4 – 4)/(1 – a)(1 – b)(1 – c)(1 – d)] ⇒ 0 |