fflpj SG Q1) α is the root of equation x2 = x – 2. Prove that α4 = 2 – 3α. Q2) α is the root of equation x2 = 2x – 3. Prove α3 = α – 6 and α2 – 2 α3 = 9. Q3) α is the root of equation 2x2 = 3x – 4. Prove 4 α 3 = α – 12.
Mikethm SG 1)a^2= a-2square both sidesa^4= a^2-4a+4a^4= (a-2) - 4a +4a^4 = 2 - 3a (proven) 2)a^2 = 2a -3multiply by aa^3 = 2a^2 -3aa^3 = 2(2a-3) -3aa^3 = a -6 (Proven)-2a^3 = -2(a-6)a^2-2a^3 = a^2 -2a +12a^2-2a^3 = (2a-3) -2a +12a^2- 2a^3 = 9 (proven)3)2a^2= 3a -4Multiply by 2a4a^3= 6a^2 - 8a4a^3 = 3(3a-4) - 8a4a^3 = a -12 (proven)