Question 126 ii 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-7 -1Also- show that -7 -1-1 -7

Now, put a = ( 7) and b = ( 1) ⇒ ( 7) Δ ( 1) = ( 7) × ( 1) 2 × ( 7) × ( 1) + ( 1) × ( 1) { ( 7)}× ( 1) + ( 1) × ( 1) = 7 14 + 1 × 7 × ( 1) + 1 7 14 7+1 ⇒ 1 ...

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Question 126 ...

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Question 126 (ii)

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
$(- 7) Δ (- 1)$
Also, show that $(- 7) Δ (- 1) \neq (- 1) Δ (- 7)$

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Solution

Now, put a = (-7) and b = (-1)
$\Rightarrow (- 7) Δ (- 1) = (- 7) \times (- 1) - 2 \times (- 7) \times (- 1) + (- 1) \times (- 1) {- (- 7)} \times (- 1) + (- 1) \times (- 1) = 7 - 14 + 1 \times 7 \times (- 1) + 1 7 - 14 - 7 + 1 \Rightarrow - 13$
Now, put a = (-1) and b = (-7)
$\Rightarrow (- 1) Δ (- 7) = (- 1) \times (- 7) - 2 \times (- 1) \times (- 7) + (- 7) \times (- 7) - (- 1) \times (- 7) + (- 7) \times (- 7) = 7 - 14 + 49 (1) \times (- 7) + 49 = 7 - 14 - 343 + 49 = - 301$
Clearly, $(- 7) Δ (- 1) \neq (- 1) Δ (- 7)$

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Question 126 (ii) 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 (−7)Δ(−1) Also, show that (−7)Δ(−1)≠(−1)Δ(−7)

Question 126 (ii)

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
$(- 7) Δ (- 1)$
Also, show that $(- 7) Δ (- 1) \neq (- 1) Δ (- 7)$