Math, asked by adi410410410, 2 months ago

find the coefficient of x⁴ in expansion of (x+1/x)³.(x+2/x²)¹⁰​

Answers

Answered by biswasyashika
0

Answer:

Hey mate !! Here is your answer

Step-by-step explanation:

The coefficient of x¹⁰ in the expansion of (1+x)²(1+x²)³(1+x³)⁴ is equal to

the coefficient of x¹⁰ in the expansion of (1+x)²(1+x²)³(1+4x³+6x⁶+4x⁹)

We can ignore the last term in the expansion (1+x³)⁴, since its exponent is

greater than 10.

= Coefficient of x¹⁰ in the expansion of (1+x)²(1+x²)³

+4∗Coefficient of x⁷ in the expansion of (1+x)²(1+x²)³

+6∗Coefficient of x⁴ in the expansion of (1+x)²(1+x²)³

+4∗Coefficient of x in the expansion of (1+x)²(1+x²)³,

Coefficient of x¹⁰ in the expansion of (1+x)²(1+x²)³=0, since the highest degree term in the expansion is 8.

Coefficient of x⁷ in the expansion of (1+x)²(1+x²)³=

Coefficient of x⁷ in the expansion of (1+2∗x+x²)(1+x²)³

=2∗Coefficient of x⁶ in the expansion of (1+x²)³

=2∗1=2,

Coefficient of x⁴ in the expansion of (1+x)²(1+x²)³=

Coefficient of x⁴ in the expansion of (1+2∗x+x²)(1+x²)³

=1*Coefficient of x⁴ in the expansion of $$(1+x²)³ +

1*Coefficient of x in the expansion of (1+x²)³

=3+3=6

Coefficient of x in the expansion of (1+2∗x+x²)(1+x²)³

=2∗ constant in the expansion of (1+x²)³

=2,

Thus ,the coefficient of x¹⁰ in the expansion of (1+x)²(1+x²)³(1+x³)⁴

=0+4∗2+6∗6+4∗2

=52.

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