10571)15
2)56
3)192
man111 singh Thanks Ketan would you like to explain it how can you get itUpvote·0· Reply ·2013-02-24 03:49:51
\hspace{-16}$If $\bf{a+b=8}$ and $\bf{ab+c+d=23}$ and $\bf{ad+bc=28}$ and $\bf{cd=12}$.\\\\ Then value of \\\\ $\bf{(i)\;\;\;a+b+c+d=}$\\\\ $\bf{(ii)\;\;ab+bc+cd+da=}$\\\\ $\bf{(iii)\; abcd=}$
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2 Answers
2305a+b = 8.......(i)
ab + c+ d = 23......(ii)
ad + bc = 28.....(iii)
cd = 12......(iv)
Adding (i),(ii),(iii),(iv) and factorizing the LHS we get:
(a+b) + (c+d) + (a+b)(c+d) = 71
Substituting the value of a+b we get :
c+d = 7.........(v)
From (iv) and (v) we get c = 4 and d = 3.
From (ii) and (v) we get ab = 16......(vi)
From (i) and (vi) we get a = 4 and b = 4.
Therefore answers are:
1)15
2)56
3)192
1057