two numbers are in the ratio of2:3.If the sum of their sqares is 468,find the numbers please answered me imediately
We do not provide immediate answers, since there is not always a teacher on duty.
Let the smaller number be x. Then the larger number is 3x/2.
Solve the equation x^2 + 9x^2/4 = 468
13x^2/4 = 468
x^2 = 144
x = 12
The larger number is 18
To find the numbers, we can set up equations based on the given information.
Let's assume the two numbers are 2x and 3x (since they are in the ratio of 2:3). Now, we can use the sum of squares equation to solve for x.
According to the problem, the sum of their squares is 468. So we can express this as an equation:
(2x)^2 + (3x)^2 = 468
Simplifying the equation:
4x^2 + 9x^2 = 468
Combining like terms:
13x^2 = 468
Now, divide both sides of the equation by 13 to solve for x:
x^2 = 36
Taking the square root of both sides:
x = ±6
Since we're dealing with ratios, we will consider positive values for x, so x = 6.
Now we can find the numbers:
The first number is 2x = 2 * 6 = 12.
The second number is 3x = 3 * 6 = 18.
Therefore, the two numbers are 12 and 18.