Advertisements
Advertisements
प्रश्न
If Δ is an operation such that for integers a and b we have a Δ b = a × b – 2 × a × b + b × b (–a) × b + b × b then find 4 Δ (–3) Also show that 4 ∆ (–3) ≠ (–3) ∆ 4.
Advertisements
उत्तर
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) × (–3)
= –12 – 2 × (–12) + (9)(12) + 9
= –12 + 24 + 108 + 9
= –12 + 141
= 129
Now, put a = –3 and b = 4
⇒ (–3) Δ 4 = (–3) × 4 – 2 × (–3) × (4) + 4 × 4{–(–3)} × 4 + 4 × 4
= (–12) + 24 + 16(3) × 4 + 16
= (–12) + 24 + 192 + 16
= 220
Clearly, 4 Δ (–3) ≠ (–3) Δ 4
APPEARS IN
संबंधित प्रश्न
Find the product, using suitable properties:
26 × (− 48) + (− 48) × (− 36)
Find the product, using suitable properties:
8 × 53 × (−125)
Find the product, using suitable properties:
625 × (− 35) + (− 625) × 65
Find the product, using suitable properties:
(− 17) × (− 29)
In a class test containing 10 questions, 5 marks are awarded for every correct answer and (− 2) marks are awarded for every incorrect answer and 0 for questions not attempted.
Mohan gets four correct and six incorrect answers. What is his score?
Find the following products: (– 18) × (– 10) × 9
(–157) × (–19) + 157 = ______.
A green grocer had a profit of ₹ 47 on Monday, a loss of ₹ 12 on Tuesday and loss of ₹ 8 on Wednesday. Find his net profit or loss in 3 days.
A multistorey building has 25 floors above the ground level each of height 5 m. It also has 3 floors in the basement each of height 5 m. A lift in building moves at a rate of 1 m/s. If a man starts from 50 m above the ground, how long will it take him to reach at 2nd floor of basement?
If Δ is an operation such that for integers a and b we have a Δ b = 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).
