Know your tricks (Part 2)

Algebra Level 1

9 1 2 91^{2} + 9 2 2 92^{2} + 9 3 2 93^{2} = = ?


The answer is 25394.

Andrew The by Andrew The , 25, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

( 92 − 1 ) 2 + 9 2 2 + ( 92 + 1 ) 2 = 3 ∗ 9 2 2 + 2 = 25394. ( a − b ) 2 = a 2 − 2 a b + b 2 , ( a + b ) 2 = a 2 + 2 a b + b 2 . h e r e a = 92 , b = 1. 9 2 2 = ( 90 + 2 ) 2 = 8100 + 2 ∗ 90 ∗ 2 + 4 = 8104 + 360 = 8464. a g a i n , a = 90 , b = 4. (92-1)^2+ 92^2+(92+1)^2=3*92^2+2=25394. ~~~\\(a-b)^2=a^2-2ab+b^2,~~(a+b)^2=a^2+2ab+b^2.~here ~a=92,~b=1.\\92^2=(90+2)^2=8100+2*90*2 +4=8104+360=8464.\\again,~~a=90,~ b=4.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Andrew The
May 25, 2015

Please, don't use a calculator to solve this...

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Karen Magallanes
May 17, 2015

91x91 = 8281 92x92 = 8464 93x93 = 25394 8281+8464+25394 = 25394

0 Helpful 0 Interesting 0 Brilliant 0 Confused

To put it neatly::.........91x91=8281,.......92x92=8464,..........93x93=9649.

```````````````````````````````````````8281+8464+9649=25394

Please correct your typos::93x93= { 9649 },```````8281+8464+ { 9649 }=25394

Niranjan Khanderia - 6 years ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...