Question

The product of two consecutive numbers is 12768 find the greater no

Answer 1

Answer:

hope it helps you mate ☺️

Step-by-step explanation:

An even number has the form [math]2k[/math] the even number before has the form [math]2k-2[/math] for some integer [math]k[/math].

[math](2k-2)×(2k)=12,768[/math]

[math]4k^2-4k=12,768 \mid ÷4[/math]

[math]k^2-k=3,192 \mid (a \pm b)^2=a \pm 2ab+b^2[/math]

[math]\left (k-\frac12 \right )^2-\frac14=3,192 \mid +\frac14[/math]

[math]\left (k-\frac12 \right )^2=\frac{12,769}{4} \mid \sqrt{}[/math]

[math]k-\frac12=\pm \frac{113}{2} \mid +\frac12[/math]

[math]k=-56 \lor 57[/math]

So the greater number is either [math]-112[/math] or [math]114[/math]. And you will see [math]-114×-112=112×114=12,768[/math].

Answer 2

Answer:

1st number = x

2nd number = (x + 1)

x + (x + 1) = 12768

x + x + 1 = 12768

2x + 1 = 12768

2x = 12768 - 1

2x = 12767

x = 12767 ÷ 2

x = 6383.5

Hence 1st number = 6383.5

2nd number = 6383.5 + 1

= 6384.5

ANS = The greater number is 6384.5

Hope it helps