Question

hey help me out with this
if a+b√p check picture ​

Answer 1

$if \: a \: + b \sqrt{p} + c \sqrt{q} = 0 \\ b \sqrt{p} + c \sqrt{q} = \: - a \\ by \:our \: intution \: we \: know \\ \: that \: sum \: of \: two \: postive \\ integers \: cant \: be \: a \: negative \\ \: number \: and \: the \: root \: value \: cant \: be \: \\ negative \: too. \\ so \: b \sqrt{p} + c \sqrt{q} = - a \: is \\ only \: possible \: when \: \\ a = b = c = 0$
Henceproved