Question

(x2 + 4x)2 + (x+2)2 - 10 = 0​

Answer 1

${( {x}^{2} + 4x) }^{2} + {(x + 2)}^{2} - 10 = 0 \\ {x}^{4} + 8 {x}^{3} + 16 {x}^{2} + {x}^{2} + 4x + 4 - 10 = 0 \\ {x}^{4} + 8 {x}^{3} + 17 {x}^{2} + 4x - 6 = 0 \\ {x}^{4} + {x}^{3} + 7 {x}^{3} + 7 {x}^{2} + 10 {x}^{2} + 10x - 6x - 6 = 0 \\ {x}^{3} \times (x + 1) + 7 {x}^{2} \times (x + 1) + 10x \times (x + 1) - 6 \times (x + 1) = 0 \\ (x + 1)( {x}^{3} + 7 {x}^{2} + 10x - 6) = 0 \\ (x + 1)( {x}^{3} + 3 {x}^{2} + 4 {x}^{2} + 12x - 2x - 6 )= 0 \\ (x + 1)( {x}^{2} \times (x + 3) + 4x \times (x + 3) - 2 \ (x + 3) )= 0 \\ (x + 1)(x + 3)( {x}^{2} + 4x - 2) = 0 \\ \\1) \: \: \: x + 1 = 0 \\ x = - 1 \\ \\ 2) \: \: \: x + 3 = 0 \\ x = - 3 \\ \\ 3) \: \: \: {x}^{2} + 4x - 2 = 0 \\ d = {4}^{2} - 4 \times 1 \times ( - 2) = 24 \\ x = \frac{ - 4 + \sqrt{24} }{2 \times 1} = \frac{ - 4 +2 \sqrt{6} }{2} = - 2 + \sqrt{6} \\ x = \frac{ - 4 - \sqrt{24} }{2 \times 1} = \frac{ - 4 - 2 \sqrt{6} }{2} = - 2 - \sqrt{6} \\ \\ answer \\ x = -1 \\ x = - 3 \\ x = - 2 + \sqrt{6} \\ x = - 2 - \sqrt{6}$

Answer 2

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