if (ad-bc)/(a-b-c+d)=(ac-bd)/(a-b+c-d) then each ratio is equal to a+b+c+d/4
Answers
(ad - bc)/(a - b - c + d) = (ac - bd)/(a - b + c - d) = (a + b + c + d)/4
Step-by-step explanation:
(ad - bc)/(a - b - c + d) = (ac - bd)/(a - b + c - d) = k
=> ad - bc = k(a - b) - k(c - d) Eq1
& ac - bd = k(a - b) + k(c - d) Eq2
Eq1 + eq2
=> ad - bc + ac - bd = 2k(a - b)
=> a(d + c) - b(c + d) = 2k(a - b)
=> (a - b)(d + c) = 2k(a - b)
=> d + c = 2k
Eq2 - Eq1
=> ac - bd - ad + bc = 2k(c - d)
=> a(c - d) + b(c - d) = 2k(c - d)
=> (a + b)(c - d) = 2k(c - d)
=> a + b = 2k
a + b + c + d = 2k + 2k
=> a + b + c + d = 4k
=> (a + b + c + d)/4 = k
(ad - bc)/(a - b - c + d) = (ac - bd)/(a - b + c - d) = k
=> (ad - bc)/(a - b - c + d) = (ac - bd)/(a - b + c - d) = (a + b + c + d)/4
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