Question

a+b^2=19 and a^2+b=13 find a and b

Answer 1

answer is a = 3 and b = 4

Answer 2

${a}^{2} \: + \: b \: = \: 13$
$a \: + \: {b}^{2} \: = \: 19$
Therefore,
$b \: = \: 13 \: - \: {a}^{2}$
$a \: + \: {(13 \: - \: {a}^{2} )}^{2} \: = \: 19$
${a}^{4} \: - \: 26 {a}^{2} \: + \: 169 \: + \: {a} \: = \: 19$
${a}^{4} \: - \: 26 {a}^{2} \: + \: a \: + \: 150 \: = \: 0$
from this, we get,
|a| = 3.
putting the value of a in equation, we get,
|b| = 4