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Question : 23 of 39

Marks: +1, -0

The sum of two numbers is 13 and the sum of their squares is

85 .

Find the numbers.

7,6
8,10
5,4
None

Solution:

Concept:

Form two equations from given conditions and solve for the two numbers.

Explanation:

Let the numbers be

x

and

y

.

Given

x + y = 13

and

x^2 + y^2 = 85

.

From the first equation,

y = 13 - x

.

Substitute into second:

x^2 + (13 - x)^2 = 85

.

Simplify:

x^2 + 169 - 26x + x^2 = 85

→

2x^2 - 26x + 84 = 0

.

Divide by 2:

x^2 - 13x + 42 = 0

.

Factor:

(x - 6)(x - 7) = 0

.

So

x = 6

or

x = 7

.

Thus the numbers are 6 and 7 (order any).

Answer:

The numbers are 6 and 7.

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