Albert said:if :
(1)$a,b\in N $, and $a>b$
(2)$a\times b =1364+(a+b)$
(3) eather $a$ or $b$ is a perfect square
can you tell which one is a perfect square ? ( $a$ or $b$ ?),and please find $a:b$
kaliprasad said:$ab-a-b = 1364$
or $ab-a-b+1 = 1365$
or $(a-1)(b-1)= 1365= 3 *5 * 7 * 13$
now we get 3 choices
choice 1
$ a= 92, b= 16$ and ratio $a::b = 23::4$
choice 2
$ a= 40, b = 36$ and $a::b = 10::9 $
choice 3
$a = 256, b= 8$ and $a::b= 32::1$
Albert said:we get 4 choices
an you got two points
10:9 and 23:4
Albert said:we get 4 choices
an you got two points
10:9 and 23:4
correction:kaliprasad said:I got 3 choices and missed the 4th
$b= 4,a = 356$ giving $a::b= 89::1$
it should beAlbert said:correction:
$a:b=32:1$ this answer is not correct
$a:b=89:1$ this answer is not correct
$a:b=23:4$ this answer is correct
$a:b=10:9$ this answer is correct
bingo !kaliprasad said:it should be
$a=456,b=4$ ratio = $114::1$
$a=196,b=8$ ratio = $49::2$
The equation used to find the ratio of a:b is a:b = a/b.
To solve the equation $1364+(a+b)=a\times b$, you can first subtract 1364 from both sides to get a+b = a*b - 1364. Then, you can rearrange the equation to get a/b = b - (1364/a). From there, you can plug in different values for a and solve for b to find the ratio a:b.
No, the values for a and b must be positive numbers in order for the equation $1364+(a+b)=a\times b$ to have a valid solution. Additionally, the values cannot be equal to each other, as this would result in division by zero.
Finding the ratio of a:b in this equation can help determine the relationship between the two variables. It can also be used to solve real-world problems involving proportions and rates.
Yes, this equation can only be used for linear relationships between a and b. If the relationship is non-linear, a different equation or method may be needed to find the ratio.