Question

If ad-bc/a-b-c+d=ac-bd/a-b+c-d,then show that each ratio =a+b+c+d/4

Answer 1

(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

Learn more:

If 2x-3y/3z+y=zy/zx=x+3z/2y-3x then prove that every ratio = x/y

brainly.in/question/11760839

(ad-bc)/(ab-c+d)=(ac-bd)

https://brainly.in/question/14802463