Question

please solve this


using binomial theorem expand [(x+y)^5 + (x-y)^5] and hence find the value of
$\sqrt{3 + 1 ^{5} } - \sqrt{3 - 1 {}^{5} }$


​

Answer 1

Answer:

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Step-by-step explanation:

ANSWER

(x+y)

5

+(x−y)

5

⇒

5

C

0

x

5

y

0

+

5

C

1

x

4

y+

5

C

2

x

3

y

2

+

5

C

3

x

2

y

3

+

5

C

4

xy

4

+

5

C

5

x

0

y

5

+

5

C

0

x

5

−

5

C

1

x

4

y+

5

C

2

x

3

y

2

+

5

C

3

x

2

y

3

+

5

C

4

xy

4

+

5

C

5

y

5

⇒2(

5

C

0

x

5

+

5

C

2

x

3

y

2

+

5

C

4

xy

4

)

⇒2[x

5

+10x

3

y

2

+5xy

4

]

⇒2x[x

4

+10x

2

y

2

+5y

4

] (equation 1)

Now, (

2

+1)

5

+(

2

−1)

5

Here, x=

2

,y=1

put in equation 1 and get

=2

2

[(

2

4

)+10(

2

)

2

+5]

=2

2

[4+20+5]

=58

2

Answer 2

Answer:

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