if x²-y²=101 then

x²+y²=?

thnx

5101

squaring both the sides

x⁴ + y⁴ -2x²y² = 10201

x⁴ + y⁴ = 10201 + 2x²y²

adding 2x²y² to both sides

(x² + y²)² = 101² + (2xy)²

now it is of the form a² + b² = c²        pythagorus triplet

now if you look at the table for pythagorean triplets                     

  (www.math.utah.edu/~alfeld/teaching/ptt.html)   (look in the 8^th line second last  value)

5101²=101²+5100²

x² + y² = 5101

PLS CORRECT IF WRONG

x²-y²=101 => (x+y)(x-y) = 101.

Since, 101 is a prime, the factorization is 101=101 * 1.

So (x+y)(x-y) = 101 * 1

Hence, x+y = 101 and x-y = 1 (since x+y and x-y are integers)

Solving we get x =51, y =50. Hence x²+y²=5101.

Very very easy...................

So x+y=101

      x-y =1

So x=51 and y=50