The number 15 is divided into two numbers, the sum of their square is equal to 117. What are the two numbers?
Answers:
x+y=15 and x^2+y^2=117
so, solve for y
y=15-x
then substitute into the function and solve
x^2+(15-x)^2=117
x^2+225-30x+x^2=117
2x^2-30x+108=0
x^2-15x+54=0
(x-6)(x-9)=0
so, x=6, x=9; therefore y=9, x=6
Although this is the long way to solve this, if you follow the methodology you will be able to solve all future problems like this.
9 + 6 = 15
9*9=81
6*6=36
81+36=117
9&6
6 and 9
6 & 9
is it 9 and 6?
9 x 9 = 81
6 x 6 = 36
total =117
i am not good at maths and this might be wrong so please don't quote me.
9 and 6, come on, stop cheating on your homework, I am sure you could have got that one on your own, I know you are smarter than that.
6 and 9
a+b=15
(a^2)+(b^2) = 117
(a^2)+(b^2) +2ab = 225
2ab = 108
(a^2)+(b^2) -2ab = 9
(a-b)^2 = 9
a-b = 3
OR
a-b = -3
a+b=15
so
2a=18
OR
2a =12
a = 9, b= 6 (OR a = 6, b=9)
so numbers are 6 and 9
Square numbers from 1 to 10 are (can't go any higher otherwise they exceed 117):
1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.
It therefore can't be either 11, 12, 13, 14 or 15, as they're too high. It also can't be 0, 1, 2, 3, or 4 because they're the numbers you would have to add to either 11, 12, 13, 14 or 15 in order to total 15. It also can't be 10 because 10^2 = 100 and no other number when squared = 17, which also knocks 5 out of the running because that would be its pair. But when you add 9^2 to 6^2 you get 117. Plus, when you add 9 and 6 you get 15. When you add the squares of 8 and 7, the only numbers left, you get 113.
No need for spectacular maths, 9 and 6 are your answers. My maths teacher used to hate it when I worked out my answers using basic common sense, she said it wasn't the mathematical way. Well screw her, it works, and it proves why the others don't.
9 and 6
The answers post by the user, for information only, UKQnA.com does not guarantee the right.