Question

27. If a, b, c and d satisfy the equations
a + 7b + 3C + 5d = 0,
8a + 4b + 6c + 2d = -16,
2a + 6b + 40 + 8d = 16 and
5a + 3b + 7c + d = -16, then (a + d)(b + c) equals
(A) 0
(B) 16
(C) -16
(0) -64​

Answer 1

Given :    a + 7b + 3C + 5d = 0, 8a + 4b + 6c + 2d = -16, 2a + 6b + 4c + 8d = 16 and 5a + 3b + 7c + d = -16,

To find :  Value of (a + d)(b + c)

Solution:

a + 7b + 3C + 5d = 0,     Eq1

8a + 4b + 6c + 2d = -16,   Eq2

2a + 6b + 4c + 8d = 16     Eq3

5a + 3b + 7c + d = -16,      Eq4

Eq1 + Eq4

=> 6(a + d) + 10(b + c)  =  -16     Eq5

Eq2 + Eq3

=> 10(a + d) + 10(b + c)  =  0      Eq6

Eq6 - Eq5

=> 4(a + d) = 16

=> (a + d)  = 4

=> (b + c)  = -4

(a + d)(b + c) = 4(-4) = -16

(a + d)(b + c)  = -16

option C is Correct

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