(a - b)3 + (b - c)3 + (c - a)3 কে উৎপাদকে বিশ্লেষণ করুন ।

(a - b)³ + (b - c)³ + (c - a)³ কে উৎপাদকে বিশ্লেষণ করুন ।

A 9 (a -b) (b-c) (c-a)

B 3 (a-b) (b-c) (c-a)

C 2(a-b) (b-c) (c-a)

D (a-b) (b-c) (c-a)

Solution

Correct Answer: Option B

(a - b)³ +(b -c)³+ (c − a)³
(a - b)=x, (b-c) = y, (c-a)=z ধরে পাই,
x+y+z=a-b+b-c+c-a=0
∴ x+y=-z
⇒ (x + y)² = -z³
⇒ x³ + y³ + 3xy (x + y) = -z³
⇒x³+y³+z³=3xyz [since, ∴ x+y=-z ]
∴ (a-b)³+(b-c)³+(c-a)³=3(a-b)(b-c)(a-b)

Solution

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