Maharashtra State BoardHSC Science (General) 11th
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Answer the following: (a + bx) (1 − x)6 = 3 − 20x + cx2 + ..... then find a, b, c - Mathematics and Statistics

Sum

Answer the following:

(a + bx) (1 − x)6 = 3 − 20x + cx2 + ..... then find a, b, c

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Solution

Consider, (a + bx) (1 – x)6

= a(1 – x)6 + bx (1 – x)6

= a(1 – 6C1 x + 6C2 x26C3 x3 + …) + bx(1 – 6C1 x + 6C2 x26C3 x3 + …)

= a(1 – 6x + 15x2 – 20x3 + …) + bx(1 – 6x + 15x2 – 20x3 + …)

= a + (b – 6a)x + (15a – 6b)x2 + … …(i)

Since, (a + bx) (1 – x)6 = 3 – 20x + cx2 + …

∴ a + (b – 6a)x + (15a – 6b)x2 + …

= 3 – 20x + cx2 +…     …[From (i)]

Equating both sides, we get

a = 3, b – 6a = – 20, 15a – 6b = c

∴ a = 3, b = –2 , c = 15(3) – 6(–2) = 57

Concept: General Term in Expansion of (a + b)n
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 4 Methods of Induction and Binomial Theorem
Miscellaneous Exercise 4 | Q II. (24) | Page 86
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