Question

the difference between two positive numbers is 5 and the square of their sum is 169

Answer 1

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Hey Mate!!

Let the 2 numbers be x and y.

x - y = 5

=> x = 5 + y ........(1)

$({x + y)}^{2}$ = 169

=> x + y = √169

=> x + y = 13 .......(2)

By substituting (1) in (2),

x + y = 13

=> 5 + y + y = 13

=> 2y = 13 - 5

=> 2y = 8

=> y = 8 ÷ 2

=> y = 4 ........(3)

By substituting (3) in (2),

x + y = 13

=> x + 4 = 13

=> x = 13 - 4

=> x = 9

Thus, the 2 numbers are 4 and 9.