Question

Given the sum of two numbers equal to 16 and the sum of their squares equal to 160 find the numbers

Answer 1

the numbers are 4 and 12

Explanation:

Given that

x + y = 16 ---------------- eq1

x^2 + y^2 = 160 -------- eq2

From eq1:

x = 16-y

Putting in eq2

(16 - y)^2 + y^2 -160 = 0

256 -32y + y^2 +y^2 - 160 = 0

96 -32y +2y^2 = 0

Taking 2 common:

48 - 16y + y^2 = 0

48 - 12y - 4y +y^2 = 0

12(4 - y) -y(4 - y)= 0

(12 -y) (4 - y) = 0

So weather:

y=4

OR

y = 12

Now put vaules of y in eq1

x + 4 = 16 =====> x = 12

x + 12 = 16=====> x = 4

So the numbers are 4 and 12

i hope it will help YOU!