Question

The sum of two numbers is 10.the sum of the squares of the numbers is 68.find the two numbers?

Answer 1

Answer:

The answer is 8 and 2.

8 + 2 = 10

{8}^{2} = 64

{2}^{2} = 4

64 + 4 = 68

Answer 2

Answer :

2 and 8

Step-by-step explanation :

   Let the two numbers be x and y.

Given,

• x + y = 10
• x² + y² = 68

x + y = 10

squaring on both sides,

(x + y)² = 10²

x² + y² + 2xy = 100

68 + 2xy = 100

2xy = 100 - 68

2xy = 32

xy = 32/2

xy = 16

x = 16/y

=> x + y = 10

    $\frac{16}{y} +y=10 \\\\ \frac{16+y^2}{y} =10 \\\\ 16+y^2=10y \\\\ y^2-10y+16=0 \\\\ y^2-2y-8y+16=0 \\\\ y(y-2)-8(y-2)=0 \\\\(y-2)(y-8) = 0\\\\ y=2,8$

If y = 2, x = 8

  y = 8, x = 2

∴ The two numbers are 2 and 8.

Verification :

=  x² + y²

=  2² + 8²

=  4 + 64

=  68  ✔