Question

If a + b = 4 and ab = -12, find (1) a - b (ii) a2 - b2.​

Answer 1

Answer:

(a+b)2=a2+2ab+b281=-44+a2+b2a2+b2=125(a-b)2=a2-2ab+b2(a-b)2=125-2(-22)(a-b)2=169(a-b)=13a2-b2=(a+b)(a-b)a2-b2=(9)(13)a2-b2=117  

Answer 2

If a + b = 4

and ab = -12

then,

(a + b) ² = a² + b² + 2ab

4² = a ²+b² + 2ab

16 = a² + b² +2 × -12

16 = a² + b² -24

a² + b²= 24 +16

a² + b² = 40

now,

(a - b) ² = a² + b² - 2ab

a² - b² = 40 - 2(-12)

a² - b² = 40 +24

a²- b² = 64

a -b = +8 and -8