the difference between two positive numvers is 2 and the difference between their squares is 40.
taking x to be the smaller of the two numbers, form an equation in x and solve it.
thank you in advance!
Just translate the English into "math"
<the difference between two positive numvers is 2 > --->
smaller number is x
larger number is x+2
<the difference between their squares is 40> ---->
(x+2)^2 - x^2 = 40
now solve that quadratic.
x=9! thankyou for your help!
x=9
To solve this problem, let's assume that the two positive numbers are 'x' and 'y' (where x is the smaller number).
According to the given information, the difference between the two positive numbers is 2. We can write this as an equation:
y - x = 2 ---- Equation [1]
The difference between the squares of the two numbers is 40. We can write this as:
y^2 - x^2 = 40
Now, let's solve the equation.
Step 1: Rearrange Equation [1] to solve for 'y':
y = x + 2
Step 2: Substitute the value of y from Step 1 into the second equation:
(x + 2)^2 - x^2 = 40
Step 3: Expand and simplify the equation:
x^2 + 4x + 4 - x^2 = 40
Step 4: Eliminate the x^2 terms:
4x + 4 = 40
Step 5: Subtract 4 from both sides of the equation:
4x = 36
Step 6: Divide both sides by 4:
x = 9
Now that we have found the value of x, we can substitute it back into Equation [1] to find y:
y - 9 = 2
y = 11
Therefore, the smaller number 'x' is 9 and the larger number 'y' is 11.