Question

please solve this with full explanation. no spam​

Answer 1

Answer:

396

Step-by-step explanation:

x + 1/4x = 3

4x² - 12x + 1 = 0

this is a quadratic equation of form ax²+bx+c = 0

so, x = [-b±√b²-4ac]/2a

x = 12±√(144 - 16)/2*4 = 12 ±√128/8 = 12±8√2/8 = 3/2 ± √2

if x = 3/2 + √2,

x³ = (3/2 + √2)³ = (3/2)³ + 3(3/2)²√2+3*3/2*(√2)² + (√2)³

                         = 27/8 + 27√2/4 + 9 + 2√2

                          = (27/8 + 9) + √2(27/4 + 2)

                         = 99/8 + 35√2/4 = 1/8[99 + 70√2]

16x³ = 16 * 1/8[99 + 70√2] = 2[99 + 70√2] = 198 + 140√2

4x³ = 4 *  1/8[99 + 70√2] = [99 + 70√2]/2

1/4x³ = 1/[99 + 70√2]/2 = 2/[99 + 70√2] = 2[99 - 70√2]/[99 + 70√2] [99 -  

                                                                                                               70√2]

           = 2[99 - 70√2] /  [9801 - 9800] = 2[99 - 70√2]

16x³ + 1/4x³ = 2[99 + 70√2] + 2[99 - 70√2] = 2*198= 396.

If you take x = 3/2 - √2 as well then also

16x³ + 1/4x³ will be equal to 396.