Question

State whether the statement is true (T) or false (F).
The difference of the squares of two consecutive numbers is their sum.

• A. True
• B. False

Answer 1

The correct option is A True

Let the two consecutive numbers be $x$ and $x+1$

Thus, $(x+1{)}^2=x^2+1+2x$ [$\because (a+b{)}^2=a^2+b^2+2ab$]

Therefore, the difference of squares of the two numbers is :

$(x+1{)}^2-x^2$

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

$=2x+1$

$=x+x+1$

$=\left(x\right)+(x+1)$

Hence, the given statement is true.