two numbers are in the ratio of2:3.If the sum of their sqares is 468,find the numbers
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Let's assume the two numbers are 2x and 3x, where x is a constant.
According to the given information, the sum of their squares is 468.
Therefore, we can write the equation as follows:
(2x)^2 + (3x)^2 = 468
Expanding the equation:
4x^2 + 9x^2 = 468
Combining like terms:
13x^2 = 468
Dividing both sides of the equation by 13:
x^2 = 36
Taking the square root of both sides:
x = ±6
Since x represents a positive constant, we can conclude that x = 6.
Now, substituting the value of x into the expressions for the numbers:
2x = 2 * 6 = 12
3x = 3 * 6 = 18
Therefore, the two numbers are 12 and 18.
To solve this problem, we need to set up a system of equations based on the given information and then solve for the unknown numbers.
Let's represent the numbers as 2x and 3x, where x is a common ratio. Given that the sum of their squares is 468, we can write the equation:
(2x)^2 + (3x)^2 = 468
Expanding and simplifying, we get:
4x^2 + 9x^2 = 468
13x^2 = 468
x^2 = 468/13
x^2 = 36
To find x, we take the square root of both sides:
x = √(36)
x = 6
Now, substituting the value of x back into our representation of the numbers, we find:
First number = 2x = 2(6) = 12
Second number = 3x = 3(6) = 18
So, the two numbers are 12 and 18.
x/y = 2/3
or
x = 2y/3
x^2+y^2 = 468
4y^2/9 + 9 y^2/9 = 468
13 y^2 = 468*9
y = 3 sqrt(468/13)= 3 sqrt (36)
y = 18
x = 12