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2 solutions
I do the same way :D
No need to use common sense too.
From LHS, we get x= -1 and x= -a
Take x= -1 so as to eliminate 'a'
Then,
=> (-1+1)(-1+a) = (-1)^2 + (-1)b - 6
=> 0 = 1-b-6
=> b= -5
x 2 + ( a + 1 ) x a = x 2 + b x − 6 → x 2 − x 2 + ( a + 1 − b ) x + a + 6 = 0 → ( a + 1 − b ) x + a + 6 = 0 → a = − 6 → ( − 6 + 1 − b ) x = 0 → ( − 5 − b ) x = 0 → − 5 − b = 0 → b = − 5 .
Solution:
We know that the given equation above is equal to:
( x + 1 ) * ( x + a ) = x 2 + b x − 6
By using common sense, a = − 6
So,
x 2 − 5 x − 6 = x 2 + b x − 6
t h e r e f o r e ,
b = − 5 a n s .