Question 126 i If - is an operation- such that for integers a and b- We have a - b-a - b-2 - a - b-b - b-a - b-b - b- then find 4 -3Also- show that 4 -3 -3 - 4

We have, a Δ b = a × b 2 × a × b + b × (b) ( a) × b + b × b Now, put a = 4 and b = ( 3) 4 Δ ( 3) = 4 × ( 3) 2 × 4( 3) + ( 3) × ( 3) × ( 4) × ( 3) + ( 3) × ( ...

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Question 126 ...

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Question 126 (i)

If $Δ$ is an operation, such that for integers a and b. We have $a Δ b = a \times b - 2 \times a \times b + b \times b (- a) \times b + b \times b,$ then find
$4 Δ (- 3)$
Also, show that $4 Δ (- 3) \neq (- 3) Δ 4$

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Solution

We have, $a Δ b = a \times b - 2 \times a \times b + b \times (b) (- a) \times b + b \times b$
Now, put a = 4 and b = (-3)
$4 Δ (- 3) = 4 \times (- 3) - 2 \times 4 (- 3) + (- 3) \times (- 3) \times (- 4) \times (- 3) + (- 3) \times (- 3) = - 12 - 2 \times (- 12) + (9) (12) + 9 = - 12 + 24 + 108 + 9 = 129$
Now, put a = -3 and b = 4
$\Rightarrow (- 3) Δ 4 = (- 3) \times 4 - 2 \times (- 3) \times (4) + 4 \times 4 [- (- 3)] \times 4 + 4 \times 4 = (- 12) + 24 + 16 (3) \times 4 + 16 = (- 12) + 24 + 192 + 16 = 220$
Clearly, $4 Δ (- 3) \neq (- 3) Δ 4$

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Question 126 (i) If Δ is an operation, such that for integers a and b. We have aΔb=a×b−2×a×b+b×b (−a)×b+b×b, then find 4 Δ (−3) Also, show that 4 Δ (−3) ≠ (−3) Δ 4

Question 126 (i)

If $Δ$ is an operation, such that for integers a and b. We have $a Δ b = a \times b - 2 \times a \times b + b \times b (- a) \times b + b \times b,$ then find
$4 Δ (- 3)$
Also, show that $4 Δ (- 3) \neq (- 3) Δ 4$