Problems based on Numbers Test 5

Question : 4 of 40

Marks: +1, -0

The product of two numbers is 45 and the sum of their squares is 106. What are the numbers?

Solution:

Let the two numbers be x and y; then

xy = 45

...(i)

x^2 + y^2 = 106

...(ii)

(x + y)^2 = x^2 + y^2 + 2xy

= 106 + 2 × 45 = 196

∴ x + y = 14

...(iii)
Now,

(x - y)^2 = x^2 + y^2 - 2xy

= 106 - 2 × 45 = 16

∴ (x - y) = 4

...(iv)
Solving equations (iii) and (iv), we get x = 9 and y = 5
Hence, numbers are 9, 5.

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