An algebra problem by nishant kumar

Algebra Level 1

Two consecutive numbers are 8 and 9. Find the difference of their squares.

(You will truly deserve the points when you find the answer without calculating their squares .)

17 18 16 20

Nishant Kumar by nishant kumar , 21, India

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5 solutions

Azadali Jivani
Jan 23, 2015

(9^2 -8^2) = (9+8)(9-8) =(9+8)= 17

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Angela Fajardo
Jan 26, 2015

x^2 - y^2 = (x + y)(x - y) <= (difference of two squares, (special products, factoring)

let: x = 9 , y = 8

Then substitute

9^2 - 8^2 = (9 + 8)(9 - 8)

9^2 - 8^2 = (17)(1)

9^2 - 8^2 = 17

To make sure

9^2 - 8^2 = (9 + 8)(9 - 8)

81 - 64 = 17

17 = 17

So their difference is 17

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Nishant Kumar
Jan 23, 2015

If the two consecutive numbers are x and y, then the difference of their squares is given by x + y. .

Here, x = 8 and y = 9. .

8 + 9 .

Therefore the required answer = 17

1 Helpful 0 Interesting 0 Brilliant 0 Confused

I did this mentally.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

well then i deserve the points..

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

=(9+8)(9-8)

=(17)(1)

=17

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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