Let the two numbers be x and y, y being the bigger number. From the given information,
x2 + y2 = 208 ..... (i)
y2 = 18x ..... (ii)
From (i), we get y2=208 - x2. Putting this in (ii), we get,
208 - x2 = 18x
x2 + 18x - 208 = 0
x2 + 26X - 8X - 208 = 0
x(x + 26) - 8(x + 26) = 0
(x - 8)(x + 26) = 0
x can't be a negative number , hence x = 8
Putting x = 8 in (ii), we get y2 = 18 x 8=144
y = 12, since y is a positive integer
Hence, the two numbers are 8 and 12.
Jasmine G. the sum of two numbers is 20 and the sum of their squares is 272. find the numbers I need help with to solve the equation and getting a statement like what to represent
2 Answers By Expert Tutors
So we have to translate the words into Math symbols.
Sum of two numbers is 20. This means adding 2 numbers, which we don't know, gets us 20. So, when we don't know numbers, we use variables and come up with:
Next they say, the sum of their squares is 272. Same numbers, still the sum, but now it is of their squares, we now we write:
Now we have two equations, we can use the first one so solve for one of the variables, I'll choose to solve for X since it is the most common. To do that, I subtract Y from both sides of the equal sign and end up with:
Now I take this equation and plug it into the equation with the Squares:
We have to do the multiplication here so I'm going to expand it so it is easier to see:
(20 - Y)(20 - Y) + Y2 = 272
So now, we FOIL the first part and end up with:
400 - 40Y + Y2 + Y2 = 272
It is looking like its going to turn into a quadratic, so I will combine the two Y2 and bring the 272 over to the left side:
Everything has a factor of 2, so I am going to divide every term by 2, including the 0
Which gives us the two possible solutions for Y = 16,4
We then take those values and plug them back into the first equation and get our possible X values:
So we have two possible Solutions:
Lionel T. answered • 05/12/16
I love math and you will too!
Let x and y represent your two numbers.
You can rewrite the first equation so that
and substitute that into the second
400 - 40y + y2 + y2 = 272
Use the quadratic formula and you get
Your roots are 4 and 16, so one number is 4 and the other is 16.
You should double check your answer
Bingo bango bongo, you are good to go!