Question

The difference between the squares of two consecutive odd numbers is 56. Find the
numbers​

Answer 1

Answer:

let the numbers are 2x+1 and 2x+3

so, (2x+3)^2-(2x+1)^2=56

=> {(2x+3)+(2x+1)}{(2x+3)-(2x+1)=56

=> (2x+3+2x+1)(2x+3-2x-1)=56

=> (4x+4).2=56

÷> 4(x+1)=56/2=28

=> x+1=28/4=7

=> x=7-1=6

so the numbers are 2*6+1=12+1=13 and

2*6+3=12+3=15

Answer 2

Answer:

let the no. be x

let the two consecutive no. be x, x+2

ATQ,

(x+2)^2 - x^2=56

(x+2+x)*(x+2-x) =56

(2x+2)* 2=56

2x+2=56/2

2x+2=28

2x=28-2

2x=26

x=26/2

x=13

So x=13 then x=13

x+2 => 13+2=15

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