Question

Chứng tỏ `a(b+1)+b(a+1)=(a+1)(b+1)` biết `ab=1`

Answer 1

`a(b+1)+b(a+1)=(a+1)(b+1)`

`VT=ab+a+ab+b`

`=2ab+a+b`

`=2.1+a+b`

`=2+a+b(1)`

`VP=(a+1)(b+1)`

`=a(b+1)+1(b+1)`

`=ab+a+b+1`

`=1+a+b+1`

`=2+a+b(2)`

`(1)(2)=>VT=VP`.

 

Answer 2

Có: a(b + 1) + b(a + 1)

= ab + a + ab + b

= ab + a + b + 1 (do ab = 1)

= a(b + 1) + (b + 1)

= (a + 1)(b + 1)