Question #445f7

2 Answers
Feb 14, 2018

5x210x2=0

Explanation:

If the equation is ax2+bx+c=0 then alpha+beta= b/a and alpha.beta=c/a.
Comparing ax2+bx+c=0,x2+(2)x+5=0 we get alpha+beta = -2 and alpha.beta=5.
Now, 1/alpha + 1/beta =(alpha+beta)/alpha.beta= -2/5.
Hence new equation is:
x2+(2)x+(25)=0
Or,5x210x2=0

Feb 14, 2018

see a solution process below;

Explanation:

Let A and B be alpha and beta respectively..

x22x+5=x2(A+B)x+AB

A+B=2

AB=5

When A+B and 1A+1B are the roots of the equation,

The expression becomes;

x2(A+B+(1A+1B)x+[(A+B)(1A+1B)]

Therefore;

x2(A+B+(A+BAB)x+[(A+B)(A+BAB)]

Substituting the values;

x2(2+25)x+(225)

x2(125)x+45

Multiply through by 5

5x212x+4

Hope this helps!