Find the quadratic function ...

3x2 - y2 = 9

x2 + 2y2 = 38

Step-by-step explanation:

3x2 - y2 = 9 ... (1)

x2 + 2y2 = 38 ... (2)

Let x^2 = a and y^2 = b

: - the two equations becomes

3a - b = 9 ... (3)

a + 2b = 38 ... (4)

Multiplying (4) by 3

3a + 6b = 114 ... (5)

Substracting (3) from (5)

3a - 3a + 6b - (-b) = 114 - 9

6b + b = 105

7b = 105

b = 105/7

b = 15

And 3a - b = 9 putting b = 15

3a - 15 = 9

3a = 15+9

3a = 24

a = 24/3

a = 8

And

x^2 = a

x^2 = 8

x = √8

x = √ (4*2)

x = 2√2

Also y^2 = b

y^2 = 15

y = √15