Question

If a^2+4b^2+6a+4b+10=0 find a/b​

Answer 1

$Given \: a^{2}+4b^{2}+6a+4b+10=0$

$\implies a^{2} + 6a + 9 + 4b^{2}+4b+1 = 0$

$\implies (a^{2}+2\times a \times 3+3^{2})+[(2b)^{2} + 2\times 2b \times 1 + 1^{2}] = 0$

$\implies (a+3)^{2} + ( 2b + 1 )^{2} = 0$

$\therefore a + 3 = 0 \:and \: 2b+1 = 0$

$\implies a = -3 \:and \: b = \frac{-1}{2}$

Therefore.,

$\green{ a = -3 \:and \: b = \frac{-1}{2}}$

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