Let `a` and ` b` are the roots of the equation `x^2-10 xc -11d =0` and those of `x^2-10 a x-11 b=0 ,dot` are c and d then find the value of `a+b+c+d

Options

A. 1220
B. 1110
C. 1210
D. 1310

Answer

C

Explanation

It is given that c and d are roots of `x^(2) - 10 ax - 11b = 0` and a and b are roots of `x^(2)-10cx -11d = 0`
`therefore" "c+d=10a and a+b=10c`
`rArr" "c+d+a+b = 10(a+c)and, c+d-a-b=10a - 10c`
`rArr" "b+d = 9(a+c) and, b-d = 11(c-a)" "...(i)`
Again, c is a root of `x^(2)-10ax - 11b = 0` and a is a root of `x^(2) - 10 cx - 11 d = 0`.
`therefore" "c^(2)-10ac - 11b = 0 and a^(2) - 10ac -11d = 0`
`rArr" "(c^(2)-a^(2))=11(b-d)`
`rArr" "(c-a)(c+a) = 11 (b-d)`
`rArr" "c+a = 121" "[because b-d = 11 (c-a)"from(i)"]`
`rArr" "b+d = 1089" "[because b+d = 9 (a+c_"from(i)"]`
`therefore" "a+b+c+d = 2110`