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If the equations x²-10cx-11d=0 are a,b and those of x²-10ax-11b=0 are c,d then value of a+b+c+d , is (where a,b,c and d are distinct number)
If the equations x²-10cx-11d=0 are a,b and those of x²-10ax-11b=0 are c,d then value of a+b+c+d , is (where a,b,c and d are distinct number)

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3 years ago

Arun
25768 Points
```							  a2 - 10acx - 11d = 0 c2 - 10acx - 11b = 0   subtract them ......   a2 - c2 = 11 ( d - b )    ........ (1)   a + b = 10c, ab = - 11d, c + d = 10a, cd =  - 11b   a + b + c + d  = 10 ( a + c ) ...... (2) b + d = 9 ( a + c ) ....... (3)   Also,   abcd = 121bd so  ac = 121   from result (1) & (3)  .....  ( b + d ) ( a - c ) / 9 = 11 ( d - b )  ( a - c ) / 99 = ( d - b ) / ( b + d )   Simplifying. ........... a2 + c2  - 20 ac - 11 ( b + d ) = 0   ( a + c )2 - 22ac - 11 ( a + c ) 9 = 0 substutuing dat ac = 121 u get finally (a+c)2 - 99 (a+c) - 2662 = 0   This is a quadratic in a+c solving u get a  +  c = 121     Go to result  :::   a + b + c + d = 10 ( a + c )  = 1210
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3 years ago
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