solve the following equation for x: 1/x+1+2/x+2=4/x+4,is not equal to -2,-4
Answers
Answered by
3
1/x+1 + 2/x+2 = 4/x+4
x+2 + 2x + 2 / x² + 2x + x + 2 = 4/x+4
3x+4 / x²+3x+2 = 4/x+4
3x²+12x+4x+16 = 4x²+12x+8
3x²+16x+16 = 4x²+12x+8
4x² - 3x² + 12x - 16x + 8 - 16 = 0
x² - 4x - 8 = 0
x = - 4 ± √[(- 4)² - 4*1*-8] / 2*1
x = - 4 ± √(16 + 32) / 2
x = - 4 ± √48 / 2
x = - 4 ± 6.93 / 2
x = - 4 + 6.93 / 2 or - 4 - 6.93 / 2
x = 2.93/2 or - 10.93/2
x = 1.465 or -5.465
x+2 + 2x + 2 / x² + 2x + x + 2 = 4/x+4
3x+4 / x²+3x+2 = 4/x+4
3x²+12x+4x+16 = 4x²+12x+8
3x²+16x+16 = 4x²+12x+8
4x² - 3x² + 12x - 16x + 8 - 16 = 0
x² - 4x - 8 = 0
x = - 4 ± √[(- 4)² - 4*1*-8] / 2*1
x = - 4 ± √(16 + 32) / 2
x = - 4 ± √48 / 2
x = - 4 ± 6.93 / 2
x = - 4 + 6.93 / 2 or - 4 - 6.93 / 2
x = 2.93/2 or - 10.93/2
x = 1.465 or -5.465
Similar questions