Question

prove that [a+1÷a]^2 - [a-1÷a]^2=4​

Answer 1

Step-by-step explanation:

(a+1/a) ^2-(a-1/a)^2=4

(a^2+1/a^2+2×a×1/a)-(a^2+1/a^2-2×a×1/a)=4

(a^2+1/a^2+2)-(a^2+1/a^2-2)=4

a^2+1/a^2+2-a^2-1/a^2+2=4

2+2=4

4=4

Answer 2

$(a + \frac{1}{a} )^{2} - \: (a + \frac{1}{a} )^{2}$

$((a + \frac{1}{a}) + (a - \frac{1}{a}) \times ((a + \frac{1}{a}) - (a - \frac{1}{a}))$

because

(a+b)(a-b)=a^2-b^2

back to the expression

$(2a) \times (a + \frac{1}{a} - a + \frac{1}{a})$

$2a( \frac{2}{a})$

=4

Hence proven.

Please mark my answer brainliest