Question

Escreva as equações biquadradas na forma geral. Em seguida, resolva-a
A) x² ( x² - 10 ) + 9 = ( x + 1 ) ( x - 1 )

B) x ( 2x² - 2x ) = -x² ( x² - 2x + 1 )

C) 2 ( x² + 6 ) = ( x² + 6)²

D) (x² - 3) ( x² + 1) = - 2 ( x² + 3) + 3

Answer 1

Resposta:

A) x² ( x² - 10 ) + 9 = ( x + 1 ) ( x - 1 )

${x}^{4} - 10 {x}^{2} + 9 = {x}^{2} - x + x - 1 \\ {x}^{4} - 10 {x}^{2} + 9 = {x}^{2} - 1 \\ {x}^{4} - 10 {x}^{2} + 9 - {x}^{2} + 1 \\ = {x}^{4} - 11 {x}^{2} + 10$

B) x ( 2x² - 2x ) = -x² ( x² - 2x + 1 )

$2 {x}^{3} - 2 {x}^{2} = - {x}^{4} + 2 {x}^{3} - {x}^{2} \\ 2 {x}^{3} - 2 {x}^{2} + {x}^{4} - 2 {x}^{3} + {x}^{2} \\ = {x}^{4} - {x}^{2}$

C) 2 ( x² + 6 ) = ( x² + 6)²

$2 {x}^{2} + 12 = {x}^{4} + 12 {x}^{2} + 36 \\ 2 {x}^{2} + 12 - {x}^{4} - 12 {x}^{2} - 36 \\ = - {x}^{4} - 10 {x}^{2} - 24$

D) (x² - 3) ( x² + 1) = - 2 ( x² + 3) + 3

${x}^{4} + {x}^{2} - 3x {}^{2} - 3 = - 2 {x}^{2} - 6 + 3 \\ {x}^{4} - 2 {x}^{2} - 3 = - 2 {x}^{2} - 3 \\ {x}^{4} - 2 {x}^{2} - 3 + 2 {x}^{2} + 3 \\ = {x}^{4}$