Simplicity has no limit

x^2-y^2=151

(x+y)(x-y)=151

since 151 is prime number

(x+y)(x-y)=1*151

the sum of any two no. will be greater than its difference

x+y=151 x-y=1

by elimination method, x=76,y=75

xy=5700

Let $x=n+1$ and $y=n$ :

$(n+1)^2-n^2=151$

$n^2+2n+1-n^2=151$

$2n+1=151$

$2n=150$

$n=75$

Plugging the values back into $x$ and $y$ we get $x=76$ and $y=75$ , therefore $xy=(76)(75)=\boxed{5700}$

If there are two numbers n and (n+1) , then the difference between there squares is (2n+1) always. Here, 2n+1=151, so n=75 and automatically other number becomes 76. 75×76=5700.

difference between sqs of two consecutive nos is their sum.Sum is given 151 so nos are 75nd76.Ans=sq of 75 +75=5700

The only fact we need to know is that prime numbers have only 2 factors i.e. 1 and itself.