Question

If A={X: 3X+ 6 ≥ 9, X∈N } and B={X: -5X > -15, X∈N}, find A∩B

Answer 1

Step-by-step explanation:

⇒Sum,S=α+β<6

⇒α+β2<3

⇒2a2<3

⇒a<3 ...(i)

Again, product, P=αβ

⇒P<9⇒αβ<9

⇒a2+a−3<9

⇒a2+a−12<0

⇒(a−3)(a+4)<0

⇒−4<a<2 ..(ii)

Again, D=B2−4AC≥0

⇒(−2a)2−4.1(a2+a−3)≥0

⇒4a2−4a2−4a+12≥0

⇒−4a+12≥0⇒a≤3 ...(iii)

Again, = af(3)>0

⇒1.[(3)2−2a(3)+a2+a−3]>0

⇒9−6a+a2+a−3>0

⇒a2−5a+6>0

⇒(a−2)(a−3)>0

∴a∈(−∞,2)∪?(2,∞) ...(iv)

From Eqs. (i),(ii),(iii), and (iv), we get a∈(−4,2).

Note There is correction in answer