Explanation
3x + y = 21 ... (i);
xy = 30 ... (ii)
From (ii), y = 30/x
. Putting the value of y in (i), we have
3x + 30/x = 21
⟹ 3x2 + 30 = 21x
3x2 - 21x + 30 = 0
3x2 - 15x -6x + 30 = 0
3x(x - 5) - 6(x - 5) = 0
(3x - 6)(x - 5) = 0
3x - 6 = 0 ⟹ x = 2.
x - 5 = 0 ⟹ x = 5.
If x = 2, y = 30/2 = 15;
If x = 5, y = 30/5 = 6.
3x + y = 21 ... (i);
xy = 30 ... (ii)
From (ii), y = 30/x
. Putting the value of y in (i), we have
3x + 30/x = 21
⟹ 3x2 + 30 = 21x
3x2 - 21x + 30 = 0
3x2 - 15x -6x + 30 = 0
3x(x - 5) - 6(x - 5) = 0
(3x - 6)(x - 5) = 0
3x - 6 = 0 ⟹ x = 2.
x - 5 = 0 ⟹ x = 5.
If x = 2, y = 30/2 = 15;
If x = 5, y = 30/5 = 6.