Hi everyone. So, I'm going to take an important maths exam next month (it could change my life forever) and I'm studying maths by myself with some past exam papers. I'm trying to understand every problem in every exam, and the topics vary a lot. I came across this one:
We are to find the value of x⁴+y⁴+z⁴ when x, y and z are real numbers which satisfy the following three equalities:
x+y+z = 3
x²+y²+z² = 9
xyz = -2
Firstly, it follows from the first two equalities that:
xy+yz+zx = A
Next, using
(x²+y²+z²)² = x⁴+y⁴+z⁴+B = {(xy)²+(yz)²+(zx)²}
we have
x⁴+y⁴+z⁴ = C
I need to find A, B and C.
I don't know where to start. It's the first time I find a problem like this in the papers. Also, I don't really understand the "it follows from the first two equalities that..." part.
And how are these types of problems called? I'm asking so I can search for more to practice for the exam.
Thanks in advance.
We are to find the value of x⁴+y⁴+z⁴ when x, y and z are real numbers which satisfy the following three equalities:
x+y+z = 3
x²+y²+z² = 9
xyz = -2
Firstly, it follows from the first two equalities that:
xy+yz+zx = A
Next, using
(x²+y²+z²)² = x⁴+y⁴+z⁴+B = {(xy)²+(yz)²+(zx)²}
we have
x⁴+y⁴+z⁴ = C
I need to find A, B and C.
I don't know where to start. It's the first time I find a problem like this in the papers. Also, I don't really understand the "it follows from the first two equalities that..." part.
And how are these types of problems called? I'm asking so I can search for more to practice for the exam.
Thanks in advance.