Question

If the sum and difference of two expressions are 5a² – a – 4and a² + 9a – 10 respectively, then what is their LCM ?

Answer 1

Let P and Q be the two expressions. Then, 

P + Q = 5a² – a – 4                            ...(i) 

P – Q = a² + 9a – 10                         ...(ii) 

Adding (i) and (ii) 

⇒ 2P = 6a² + 8a – 14 ⇒ P = 3a² + 4a – 7 = (a – 1) (3a + 7) 

From (i), Q = (5a² – a – 4) – (3a² + 4a – 7) = 2a² – 5a + 3 = (a – 1) (2a – 3)

∴ LCM of P and Q = (a – 1) (2a – 3) (3a + 7).