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

Options

A. ` 2 sqrt(2) - 5`
B. `2sqrt(2) + 5`
C. `- 2sqrt(3) -5`
D. `- 2sqrt(2) + 5 `

Answer

a

Explanation

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` .