Question

25. Two consecutive positive integers have the following properties: The product of one integer and 4 times the other is equal to 24. Find the sum of the integers. (a) If 5 (b) 7​

Answer 1

letx and (x+1)be two consecutive integers.

The product of one integer and 4 times the other is 24=.

4x(x+1)= 24

4x²+4x=24

4x²+4x-24=0

simplify bye 4 :

x²+x-6=0

calculate delta: b²-4ac

1²-4(1*-6)=25

Δ is strictly positive, so the equation x²+x-6=0 has two solutions

(-b-√Δ)/2a =(-1-5)/2=-3

(-b+√Δ)/2a =(-1+5)/2 =2

the statement says "Two consecutive positive integers", x = 2

1st integer :2

2nd integer : 3

sum of integers = 5

check:

The product of one integer and 4 times the other equals 24.

1st integer=2

2nd =3

2(3*4)=24