Question

Maths 1 question of algebra

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

14

Step-by-step explanation:

For simplicity with typing, I'll use a and b instead of α and β.

Since a and b are the roots of x² - 4x + 1, it follows by the Factor Theorem that

x² - 4x + 1 = ( x - a ) ( x - b) = x² - ( a + b ) x + ab.

So a + b = 4 and ab = 1.

We want the value of

a / b  +  b / a   =   ( a² + b² ) / (ab)   =   a² + b²  (since we know ab = 1).

Squaring a + b gives us the squares we need:

16 = ( a + b )² = a² + 2ab + b² = a² + b² + 2  (again, using ab = 1)

=> a² + b² = 16 - 2 = 14.