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Question Number 199184 by Tawa11 last updated on 29/Oct/23

Commented by deleteduser1 last updated on 29/Oct/23

x=9,y=4,z=1

x=9,y=4,z=1

Commented by Tawa11 last updated on 29/Oct/23

Workings please.

Workingsplease.

Commented by deleteduser1 last updated on 29/Oct/23

Let x,y,z∈N If one of x,y or z are not perfect squares,then sum cannot be an integer ⇒z∈{1,4};z=1⇒(√x)+y=7⇒y∈{1,4}⇒y=4 ⇒(√x)=3⇒x=9 z=4⇒(√x)+y=4⇒y=1⇒x=3 (contradicts iii) Hence (x,y,z)=(9,4,1). This is the only solution for the first line.

Letx,y,z∈NIfoneofx,yorzarenotperfectsquares,thensumcannotbeaninteger⇒z∈{1,4};z=1⇒x+y=7⇒y∈{1,4}⇒y=4⇒x=3⇒x=9z=4⇒x+y=4⇒y=1⇒x=3(contradictsiii)Hence(x,y,z)=(9,4,1).Thisistheonlysolutionforthefirstline.

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