Question

Direction: If A @ B = A (A + B)2 and C $ D = 3 (C2-D2),
then
The value of (2 @ 3) $ 49​

Answer 1

$Given \: A@B = A(A+B)^{2} \: --(1)$

$Here, A = 2 \:and \: B = 3$

$2 @ 3 = 2(2+3)^{2}$

$= 2 \times 5^{2}$

$= 2 \times 25$

$= 50 \: --(2)$

$Given \: C \ D = ( C^{2} - D^{2} ) \:--(3)$

$Now, (2@3)\ 49$

$= 50 \ 49$

$= (50^{2} - 49^{2} ) \: [ From \: (3) ]$

$= ( 50 + 49 )( 50 - 49 )$

/* By algebraic identity */

$\boxed{ \pink{ x^{2}-y^{2} = (x+y)(x-y) }}$

$= 99 \times 1$

$= 99$

Therefore.,

$\red{ (2@3)\ 49 } \green { = 99 }$

•••♪

Answer 2

Answer:

99

Step-by-step explanation:

• A@B = A(A+B)²-------(1)

• A = 2 & B = 2

2@3 = 2(2+3)²

=> 2×5²

=> 2×25

=> 50-------(2)

• C$D = (C²-D²)--------(3)

• (2@3)$49

=> 50$49

=> (50²-49²) {°.° From equation (3)}

=> (50+49)(50-49)

x²-y² = (x+y)(x-y)

=> 99*1

=> 99

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