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Grade: 11

                        

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)

3 years ago

Answers : (1)

Arun
24730 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

3 years ago
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