X^22212y^2=303. Find X And Y

X^2−y^2=303. find x and y

 

\text{Given}\:\: x^2-y^2=303\\\\\\x^2-y^2=303\\\\\implies(x+y)(x-y)=303\\\\\implies(x+y)(x-y)=101\times3\\\\\\x-y=3\implies x=y+3\\\\\\x+y=101\\\\\text{substitute for x}\\\\(y+3)+y=101\\\\2y=101-3\\\\y=\dfrac{98}{2}\\\\\boxed{y=49}\\\\\\x=y+3\\\\x=49+3\\\\\boxed{x=52}\\\\\\\text{nderline{Possibility}}:\\\\\text{choose} \:\:x+y=3\:\:and\:\: x-y=101. \\\\\text{solve it similarly so yoll arrive at answer}\\\\\text{x=52 and y=-49}


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