(i) If a-b=2 and a^2+b^2=36 then find ab (ii) If a-b=2 ab =63 find a^2+b^2 and (a+b)^2

(i) If a-b=2 and a^2+b^2=36 then find ab (ii) If a-b=2 ab =63 find a^2+b^2 and (a+b)^2 [S.Chand ICSE Class 9 Chapter 3 Exercise 3.1 Expansion and Factorisation Solution ]

a-b=2

∴ (a-b)²=4

⇒ a²-2ab+b² = 4

⇒ a²+b²– 2ab =4

⇒ 36 -2ab = 4 [As a^2+b^2=36]

⇒ 36-4 =2ab

⇒ 2ab = 32

⇒ ab = $\frac{32}{2}$

⇒ ab=16

∴ ab = 16 [Ans]

If a-b=2 ab =63 find a²+b² and (a+b)²

(a-b)² = a²-2ab+b²

⟹ (a-b)² =a²+b² -2ab

⟹ (2)² =a²+b² -2(63)

⟹ 4 =a²+b² -126

⟹ 4+126=a²+b²

⟹ a²+b²= 130

∴ a²+b²= 130

Again, (a+b)²

= a²+2ab+b²

= a²+b²+2ab

=130 +2(63)

=130+126

= 256

∴ (a+b)² = 256

⟹ (a+b) =$\pm \sqrt{256}$

⟹ (a+b) =$\pm 16$

∴ (a+b) =$\pm 16$