Question

The sum of two consecutive odd number is 204 find the smallest number

Answer 1

Answer:

Let the positive integers are x and y where x > y.

As per the first statement

x (x+y) = 204

=> x^2 + xy = 204 ………..Eq 1

As per the second statement

y (x-y) = 35

=> xy - y^2 = 35 ………..Eq 2

Subtracting Eq2 from Eq1, we will get

x^2 +xy - (xy - y^2) = 204 - 35

=> x^2 + xy - xy + y^2 = 169

=> x^2 + y^2 = 169

=> x^2 + y^2 = 13^2

According to Pythagoras theorem,

Sum of square of Height and Base = to square of Hypotenues.

=> x^2 + y^2 = 13^2

Using hit and trial method we will get the value of x and y

ie. 12^2 + 5^2 = 13^2

=> 144 + 25 = 169

=> 169 = 169

So x = 12 and y = 5

Ans: 12 and 5

Answer 2

Answer:

101

Step-by-step explanation:

let 1st number be ( x+1) and second number be (x+3)

given that sum of 2 numbers is 204

x+1+x+3=204

2x+4=204

2x=204-4

2x=200

x=200/2

x=100

since 1st number is x+1=100+1=101

2nd number is x+3=100+3=103

so the numbers are 101,103

and the smallest number is 101