Question

Given, a = √5, what is (a + 1)² + (a-1)² ?

• A. 13
• B. 12
• C. 14
• D. 15

Answer 1

Answer:

B. 12

Given:

$a=\sqrt{5}$

We need to find:

$(a+1)^2+(a-1)^2$

Using the identity:

Expand:

$(a+1)^2 = a^2+2a+1$
$(a-1)^2 = a^2-2a+1$

Adding:

$(a+1)^2+(a-1)^2$
$= (a^2+2a+1)+(a^2-2a+1)$
$= 2a^2+2$

Since $(a=\sqrt{5}),$

$a^2=5$

Therefore,

$2(5)+2=12$