Question

2+3=43, 3+4=109, 7+9=1138 then 12+14

Answer 1

Answer:

12+14= 4708

Step-by-step explanation:

2 + 3 = 43

=(2 × 4) × (2 + 3) + [3 × (3 - 2)]

=(8) × (5) + [3 × (1)]

=40+3

=43

now consider 3 + 4 = 109

=(3 × 5) × (3 + 4) +(4 × (4 - 3))

=(15) × (7) + 4 × (1)

=105+4

=109

7 + 9 = 1138

=(7 × 10) × (7 + 9)+ 9 × (9 - 7)

=(70) × (16) +[9 × (2)

=1120 + 18

= 1138

we can write given terms in terms of a, b is

{(a×(b+1)}{a+b}+b(b-a)

similarly we get the answer for

12 + 14 = ?

=(12 × 15) × (12 + 14)+ [14 × (14 - 12)]

= (180) × (26) + [14 × (2)]

=4680 + 28

= 4708

Answer 2

12 + 14 = 4708

Step-by-step explanation:

The pattern followed in the given series is:

Let 'a' and 'b' be the numbers before equal sign.

a × (b + 1)(a + b) + (b(b - a))

2 + 3 = 43

⇒ 2 × (3 + 1)(2 + 3) + (3(3 - 2))

⇒ 2 × (4)(5) + (3(1))

⇒ 2 × 20 + 3

⇒ 40 + 3

∴ 43

3 + 4 = 109

⇒ 3 × (4 + 1)(3 + 4) + (4(4 - 3))

⇒ 3 × (5)(7) + (4(1))

⇒ 3 × 35 + 4

⇒ 105 + 4

∴ 109

7 + 9 = 1138

⇒ 7 × (9 + 1)(7 + 9) + (9(9 - 7))

⇒ 7 × (10)(16) + (9(2))

⇒ 7 × 160 + 18

⇒ 1120 + 18

∴ 1138

12 + 14 = ?

⇒ 12 × (14 + 1)(12 + 14) + (14(14 - 12))

⇒ 12 × (15)(26) + (14(2))

⇒ 12 × 390 + 28

⇒ 4680 + 28

∴ 4708