Question

If m^2-5/2m=-11/2,m=

Answer 1

The answer is m = ( 5 ± 3i√7) / 4

Answer 2

Answer: The required value of m is

`m=(5+√(63)i)/(4),~~~~~(5-√(63)i)/(4).`

Step-by-step explanation: We are given to find the vale of m if :

`m^2-(5)/(2)m=-(11)/(2)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

The given equation is a quadratic one, so we will be using the formula for the solution of a quadratic equation
`ax^2+bx+c=0,~a\\eq 0` as follows :

`x=(-b\pm√(b^2-4ac))/(2a).`

From equation (i), we have

`m^2-(5)/(2)m=-(11)/(2)\\\\\\\Rightarrow 2m^2-5m+11=0\\\\\Rightarrow x=(-(-5)\pm√((-5)^2-4*2*11))/(2*2)\\\\\\\Rightarrow x=(5\pm√(25-88))/(4)\\\\\\\Rightarrow x=(5\pm√(-63))/(4)\\\\\\\Rightarrow x=(5\pm√(63)i)/(4).`

Thus, the required value of m is

`m=(5+√(63)i)/(4),~~~~~(5-√(63)i)/(4).`