Question #385c9

1 Answer
Feb 7, 2018

Complex solutions:

x1=1+i32 and x2=1i32

Check the explanation for the solution using sum and product

Explanation:

x1+x2=1 and x1x2=1

x1+x2=1(x1+x2)2=1x21+x22+2x1x2=1
x21+x22+21=1x21+x22=1

So, by using sum and product we proof that the solutions are non real, because if x1 and x2 were reals, the sum of their squares couldn't be negative.

x1=a+bi
x2=abi
(this came from the fact that if a+bi is a root, so abi is a root too, and the quadratic equation has two roots)

With a and b real, and b positive.

x1+x2=1a=12
So...
x1=12+bi and x1=12bi

Lets use the product
x1x2=1(12+bi)(12bi)=1
14+b2=1b2=34b=32

Then...

x1=1+i32 and x2=1i32