Question

for what value of x, the fifth term of following expansion is equal to 105? (1/2√x-1/2)∧10

Answer 1

Given that,

The fifth term of following expansion is equal to 105.

$105=(\dfrac{1}{2\sqrt{x}}-\dfrac{1}{2})^{10}$

We need to calculate the value of x

Using general term

$T_{r+1}=^{n}c_{r}\cdot x^{n-r}\cdot y^{r}$

Where,

$T_{r+1}=105$

r = 4

n = 10

$x=\dfrac{1}{2\sqrt{x}}$

$y=-\dfrac{1}{2}$

Put the value in general equation

$105=^{10}c_{4}\cdot (\dfrac{1}{2\sqrt{x}})^{10-4}\cdot(\dfrac{1}{2})^{4}\cdot(-1)^{6}$

$x^3=\dfrac{^{10}c_{4}}{105\times2^{10}}$

$x=0.125$

Hence, The value of x is 0.125.

Answer 2

Answer:

answer is 1/8 or 0.125

Step-by-step explanation:

Given that,

The fifth term of following expansion is equal to 105.

We need to calculate the value of x

Using general term

Where,

r = 4

n = 10

Put the value in general equation

Hence, The value of x is 0.125.