Answer:
[tex]Suppose~that~the~two~numbers~are~x~and~y.\\According~to~question,\\Sum~of~the~numbers = 13\\or, x+y=13........(1)\\or, y = 13-x.......(2)\\Again,\\Sum~of~their~squares=89\\or, x^2+y^2=89\\or, (x+y)^2-2xy=89\\From~eq^n(1)~and~(2),\\13^2-2x(13-x)=89\\or, 169-26x+2x^2=89\\or, 2x^2-26x+169-89=0\\or, 2x^2-26x+80=0\\or, x^2-13x+40=0\\or, x^2-8x-5x+40=0\\or, x(x-8)-5(x-8)=0\\or, (x-5)(x-8)=0\\i.e. x=5~or~8\\When~x=5,~y=13-x=13-5=8\\When~x=8,~y=13-x=13-8=5\\So,~the~two~numbers~are~5~and~8.[/tex]
