Theory question 110
Surds(a) Express (5 + √2)/(3 − √2) − (5 − √2)/(3 + √2) in the form a + b√2.
(b) Solve the following equations simultaneously using the determinant method: 3x − y − z = −2; x + 5y + 2z = 5; 2x + 3y + z = 0.
Show the model answer
Model answer
(a) (5 + √2)(3 + √2)/7 = (17 + 8√2)/7 and (5 − √2)(3 − √2)/7 = (17 − 8√2)/7.
Difference = 16√2/7: a = 0, b = 16/7.
(b) Δ = 1; Δₓ = −8; Δᵧ = 19; Δ_z = −41.
x = −8, y = 19, z = −41.
Explanation
Check the solution in all three equations.