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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10 solutions

Julio Reyes
Sep 23, 2013

In mathematics, a binary operation is a calculation involving two elements(the operands) of a set and produce another element of the set. A basic example would be addition.

Take, 4 + 3 = 7 for example. 4 and 3 are the operands, + is the operator, and 7 is the resulting element. We have been conditioned to know the addition operator(+) tells us to take the two operands and sum them together to produce the resulting element.

Now take the operator ⊗. We don't need to have any prior knowledge of the operator since the problem defines the calculation to be done on the two operands to produce the answer.

a b = ( a × a ) ( b × b ) a⊗b=(a×a)-(b×b) .

4 3 = ( 4 × 4 ) ( 3 × 3 ) = 7 \therefore 4⊗3 = (4 \times 4) - (3 \times 3) = 7

Noreen Marpuri
Sep 22, 2013

a=4 b=3 (aXa)-(bXb) =(4X4)-(3X3) =(16)-(9) =16-9 =7

Zi Song Yeoh
Sep 27, 2013

4 2 3 2 = 7 4^2 - 3^2 = 7 .

William Cui
Sep 26, 2013

4 3 = ( 4 × 4 ) ( 3 × 3 ) 4⊗3=(4\times4)-(3\times3)

4 × 4 3 × 3 = 16 9 = 7 4\times4-3\times3=16-9=7

So, our final answer is 7 \boxed{7}

Its simply (4+3)(4-3)

Daphne Ong
Sep 22, 2013

Subs a=4, b=3 into eq., (4 4) - (3 3) = 16-9 = 7

Angel Bitanga
Sep 22, 2013

( 4 x 4 ) - (3 x 3) 16 - 9 = 7 7 is the Answer.

Unline
Sep 22, 2013

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

so the sign ⊗ means the difference between the squares of 2 values ! so 4 ⊗ 3 = ( 4 ^ 2 ) - ( 3 ^ 2 ) = 16 - 9 = 7

i wrote this cause i wanted to test if it has extra points or not !

i know that was so clear !

4⊗3=(4×4)−(3×3)

4⊗3=(16)−(9)

4⊗3=7

Zah' Kina Lashley
Sep 23, 2013

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

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