Question

Escreva na forma reduzida ax2+ bx + c= 0 as seguintes equações.
a) x2– 7 = x + 5
b) x2 + 11x = 16x – 6
c) x2+ 2x + 1 – 4x2= 12x + 9
d) x2– 20x + 100 + x.(x + 17) = 104
e) 20x2+ 7x.(3x-4) = 8x+6
f) 8x2+ 20 – x2= 6.(5-7x2) - 30
h) 5x+(7x-12)-(20+4x) + x2

Answer 1

Resposta:

$a) {x}^{2} - 7 = x + 5 \\ {x}^{2} - x = 5 + 7 \\ x {}^{2} - x = 12 \\ {x}^{2} - x - 12 = 0 \\ \\ b) {x}^{2} + 11x = 16x - 6 \\ {x}^{2} - 16x = - 6 - 11 \\ {x}^{2} - 16x = - 17 \\ {x}^{2} - 6x + 17 = 0 \\ \\ c) {x}^{2} + 2x - 1 - {4x}^{2} = 12x + 9 \\ {x}^{2} - {4x}^{2} + 2x - 12x = 9 - 1 \\ - 3 {x}^{2} - 10x + 8 = 0\\ \\ d) {x}^{2} - 20x + 100 + x.(x + 17) = 104 \\ {x}^{2} - 20x + 100 + {x}^{2} + 17x - 104 = 0 \\ {x}^{2} + {x}^{2} - 20x + 17x + 100 - 104 = 0 \\ 2 {x}^{2} - 3x - 4 = 0 \\ \\ e)20 {x}^{2} + 7x.(3x - 4) = 8 x + 6 \\ {20x}^{2} + 21 {x}^{2} - 28x = 8x + 6 \\ 20 {x}^{2} + 21 {x}^{2} - 28x - 8x - 6 = 0 \\ 41 {x}^{2} - 36x - 6 = 0 \\ \\ f)8 {x}^{2} + 20 - {x}^{2} = 6.(5 - 7 {x}^{2}) - 30 \\ 8 {x}^{2} + 20 - {x}^{2} - 30 + 42x {}^{2} \\ 8 {x}^{2} - {x}^{2} + 42 {x}^{2} + 20 - 30 = 0 \\ 49 {x}^{2} - 10 = 0 \\ \\ h)5x + (7x - 12) - (20 + 4x) + {x}^{2} \\ 5x + 7x - 12 - 20 - 4x + {x}^{2} \\ {x}^{2} + 5x + 7x - 4x - 12 - 20 \\ {x}^{2} + 8x - 32 = 0$