Question

a2+b2 +a2b2 = 3033 where a and b are positive integers and a > 0. The value of 3a +b/2
is equal to​

Answer 1

Step-by-step explanation:

${a}^{2} + {b}^{2} + {a}^{2} {b}^{2} = 3033$

${a}^{2} + {a}^{2} {b}^{2} + {b}^{2} + 1 - 1 = 3033$

${a}^{2} (1 + {b}^{2} ) + 1( {b}^{2} + 1) = 3033 + 1$

$( {a}^{2} + 1)( {b}^{2} + 1) = 3034$

$( {a}^{2} + 1)( {b}^{2} + 1) = 82 \times 37$

$( {a}^{2} + 1)( {b}^{2} + 1) = (81 + 1)(36 + 1)$

$( {a}^{2} + 1)( {b}^{2} + 1) = ( {9}^{2} + 1)( {6}^{2} + 1)$

Therefore, if a = 9, then b = 6

if a = 6 then b = 9

For a = 9 and b = 6

$3a + \frac{b}{2} = 3 \times 9 + \frac{6}{2} = 27 + 3 = 30$

For a = 6 and b = 9

$3a + \frac{b}{2} = 3 \times 6 + \frac{9}{2} = 18 + 4.5 =22.5$