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The largest real value of x, such that ...

The largest real value of x, such that
`sum_(r=0)^(4) ((5^(4-r))/((4-r)!))((x^(r))/(r!)) = (8)/(3)` is

A

` 2 sqrt(2) - 5`

B

`2sqrt(2) + 5`

C

`- 2sqrt(3) -5`

D

`- 2sqrt(2) + 5 `

Text Solution

Verified by Experts

The correct Answer is:
a
Given , ` sum_(r=0)^(4) (5^(4-r))/((4-r)!) ((x^(r))/(r!)) = (8)/(3)`
` rArr ((5+x)^(4))/(4!) = (8)/(3)`
` rArr (5+ x)^(4) = 64 = (2sqrt(2))^(4) rArr 5 + x = pm 2 sqrt(2)`
` therefore x = 2sqrt(2) - 5 or x = - 2sqrt(2) - 5`
Hence , largest real value of x is ` 2 sqrt(2) - 5` .
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