15-03-2021
Mathematics

contestada

Find the values of a, if the
coefficient of x^2 in the
expansion (1+ax)^4(2-x)^3 is 6

Respuesta :

ganjilaya2019 ganjilaya2019

15-03-2021

Step-by-step explanation:

(1 + ax)⁴(2 - x)³ = (1 + 2ax + a²x²)²(8 - 12x + 6x² - x³) =

(1 + 4a²x² + a⁴x⁴ + 4ax + 2a²x² + 4a³x³)(8 - 12x + 6x² - x³) = ... 6x² + 32a²x² - 48ax² + 16ax² ...

= ... x²(6 + 32a² - 32a) ...

32a² - 32a + 6 = 6

32a(a - 1) = 0 → 32a = 0 → a = 0 OR a - 1 = 0 → a = 1

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