For what values of A and B,the identity 7x-4=A(x-7)+B(x-2) will hold good?
Answers
Answer:
A = - 2 , B = 9
Step-by-step explanation:
Given--->
7x - 4 = A ( x - 7 ) + B ( x - 2 )
To find ---> Value of A and B
Solution--->
7x - 4 = A ( x - 7 ) + B ( x - 2 )
= A x - 7A + B x - 2B
= A x + B x - 7 A - 2 B
7 x - 4= x ( A + B ) - 7A - 2 B
If given identity holds good then
Comparing coefficients of x from both sides
A + B = 7 ..................(1)
Comparing costant term from both sides
-7A - 2B = -4
Changing the sign of whole equation
7A + 2B = 4 ...........(2)
Now we solve both eqution by substitution method
A + B = 7
B = 7 - A
Putting B = 7 - A in equation (2)
7A + 2 B = 4
7A + 2 ( 7 - A ) = 4
7 A + 14 - 2A = 4
5 A = 4 - 14
5 A = - 10
A = - 10 / 5
A = - 2
Putting A = -5 in equation (1)
A + B = 7
- 2 + B = 7
B = 7 + 2
B = 9
A=-2,B=2