Question

the sum of two numbers as well as the difference between their square is 9 find the numbers

Answer 1

Hey

Here is your answer,

Let one number be a and next number be b

We know that,
a+b= 9-------(1)

a²-b²= 9

As a²-b²= (a+b)(a-b)

So, (a+b)(a-b)= 9
But a+b= 9
(9)(a-b)= 9
a-b= 1-------(2)
Adding (1) and (2),
a+b+a-b= 9+1
2a= 10

a= 5

b= 9-5= 4


Hope it helps you!

Answer 2

let 2 nos. be x and y
x+y=9
x^2-y^2=9
x=9-y
(9-y)^2-y^2=9
81+y^2-18y-y^2=9
72=18y
y=4
now x=9-y
x=9-4=5.....
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