Mukul's binary operation

Algebra Level 1

For integers a a and b b , let ⊗ \otimes be the binary operation a ⊗ b = ( a × a ) − ( b × b ) a\otimes b=(a \times a)-(b \times b) . What is the value of 4 ⊗ 3 4\otimes 3 ?

This problem is posed by Mukul G .


The answer is 7.

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Arron Kau by Arron Kau

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16 solutions

Raja Fakirchandra
Sep 24, 2013

a⊗b=(a×a)−(b×b)

So, in 4⊗3, a = 4 & b = 3

Now, 4⊗3 becomes 

                        (4 × 4) - (3 × 3)
                        =16 - 9
                        =7
4 Helpful 0 Interesting 0 Brilliant 0 Confused
Mukesh Jha
Sep 24, 2013

Let a=4 and b=3 , ',4⊗3=(4×4)-(3×3) =16-9 =7

2 Helpful 0 Interesting 0 Brilliant 0 Confused

(4 x 4)- (3x3)

=16-9 =7

Claire Casimiro - 7 years, 8 months ago
Nao Yuki
Sep 28, 2013

a = 4 b = 3

(a . a) - (b . b) = (4 . 4) - (3 . 3) = 16 - 9 = 7

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Shankhadip Mandal
Sep 28, 2013

a=4 and b=3 so(4x4)- (3x3)=16-9=7

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Sagar Bhatia
Sep 28, 2013

given: a@b = (a a) - (b b) now, a=4, b=3 => 4@3= (4 4) - (3 3) = 16 - 9 = 7 (answer)

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Nur Azizah
Sep 28, 2013

a⊗b=(a×a)−(b×b). So, 4⊗3 = (4×4)-(3×3) = 16-9 = 7

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Nurin Zunah
Sep 27, 2013

4⊗3 = (4 x 4) - (3 x 3)

4⊗3 = 16 - 9

4⊗3 = 7

0 Helpful 0 Interesting 0 Brilliant 0 Confused

we see that: a⊗b=(axa)-(bxb) so: if a=4 and b=3 => we have: (4x4)-(3x3)=7

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Yolanda Miranda
Sep 27, 2013

( 4 * 4 ) - ( 3 * 3 ) = 7

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Terrence Whidbee
Sep 27, 2013

I multiplied a by a and b by b then subtracted the solutions

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Mohammed Magdi
Sep 26, 2013

since, our binary operation define as : a⊗b=(a×a)−(b×b) then , plug in a & b by 4 & 3 we get : 4⊗3 = (4x4) - (3x3) = 16 - 9 = 7

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Brooke Carpenter
Sep 26, 2013

You have (4 x 4) - (3 x 3). You follow the order of operations and get 16 - 9. Your answer is 7.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
David L.
Sep 25, 2013

4×4=16

3×3=9

16-9=7

QED

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Ilham Adiyaksa
Sep 25, 2013

4⊗3 = (4x4) - (3x3) = 16-9 = 7

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Adrian Wong
Sep 25, 2013

let a = 4, b = 3 , u'll get 4^2 - 3^2 = 16 - 9 = 7

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Sharad Roy
Sep 24, 2013

putting value of a=4 and b=3, we get (4 x 4) - (3 x 3) = 16 - 9 = 7

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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