CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


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
loader
B
False
loader

Solution

The correct option is A True
Let the two consecutive numbers be $$x$$ and $$x+1$$

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

Therefore, the difference of squares of the two numbers is :
$$(x+1)^{2}-x^{2}$$
$$=(x^{2}+2x+1)-x^{2}$$
$$=2x+1$$
$$=x+x+1$$
$$=(x)+(x+1)$$ 

Hence, the given statement is true.

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image