Question

If the product of two consecutive odd number is 99,find the numbers.​

Answer 1

Answer:

9 and 11

Step-by-step explanation:

Let the two consecutive odd integers be x and  x +2

x(x+2) = 99

x² + 2x = 99

x² + 2x - 99 = 0

splitting the middle term :-

x² + 11x - 9x - 99 = 0

x( x + 11) - 9(x + 11) =0

(x - 9) ( x + 11) = 0

x = 9 , x = - 11

x = 9 is the value taken here :-

x = 9

x + 2 = 9 + 2 = 11

Answer 2

Answer:

two consective odd number is (2n+1) and (2n+3)

(2n+1)(2n+3)= 96

4n2+6n+2n+3= 96

4n2+8n= 93

4n2+8n-93=0

d = b2-4ac

(8)2-4(4)(-93)

64-16(-93)

64+ 1488

1452

n = -8+_sq.root(1452)/8

n = -8+_sq.root(2×726)/8

-8+_sq.root(4×363)/8

-8+_2sq.root(3×121)/8

-4+_sq.root(3×11×11)/4

-4+_11sq.root3/4