Question

If \(\Large x^2=8x+y\) and \(\Large y^2=x+8y\), determine the numerical value of \(\Large x^2+y^2\). Assume \(\Large x\neq y\).

Answer 1

\[\large x^2 + y^2 = 9(x+y)\]

Answer 2

says numerical

Answer 3

so, what is the numerical value of it ?

Answer 4

\[\large x^2 - y^2 = 7(x-y) \implies x+y = 7 ~~~\because x\ne y \]

Answer 5

plug that in first equation ^^

Answer 6

Or multiply x^2+y^2 by x^2-y^2

Answer 7

Oh yes thats even better :)

Answer 8

:)

Answer 9

this is not my best area

can you explain this step @ganeshie8

\(\large x^2 - y^2 = 7(x-y) \implies x+y = 7 ~~~\because x\ne y\)

Answer 10

nm difference is squares.... sorry

Answer 11

yes :) just cancelled out the nonzero factor (x-y)

Answer 12

very clever