Question

Chứng minh rằng: (a x a) - ((a - 1) x (a + 1)) = 1

nguyễn huy tú help me!

Answer 1

\(\left(a.a\right)-\left[\left(a-1\right)\left(a+1\right)\right]=1\)

\(\Leftrightarrow a^2-a^2+1=1\)

\(\Leftrightarrow1=1\) ( luôn đúng )

\(\Rightarrow a\in R\)

Vậy...

Answer 2

a.a - [(a-1)(a+1)]

= [(a-1+1)a]-[(a-1)(a+1)]

= [(a-1)a + 1.a] - [(a-1)a + (a-1).1]

= (a-1)a + a - (a-1)a - (a - 1)

= a - a + 1

= 1