Question

If the cube root of 38 14 – 100 2 is rootx -rooty then what is x-y

Answer 1

Answer:

8

Step-by-step explanation:

38 14 – 100 2

= –2 2 (50 – 19 7 )

Now 1/3 (38 14 –100 2) = – (2 2 )

(50 – 19 7 )]1/3

= 1/3 (– 2) (50 – 19 7)

Now let 1/3 (50 – 19 7) x – y ...(i)

and (50 + 19 7 )

1/3 = x y ....(ii)

multiplying (i) and (ii) we get

(2500 – 2527)1/3 = x2

– y

–3 = x2

– y

y = x2

+ 3

Cubing (i) 50 – 19 7

= x3

– 3x2

y + 3xy – y y

Equation rational parts, we have

x

3

+ 3xy = 50

or x

3

+ 3x (x2

+ 3) – 50 = 0 (' y = x2

+ 3)

or 4x3

+ 9x – 50 = 0

x = 2 (by remainder theorem)

y = 7

Hence the required cube is

– 2 (2 – 7) 14 – 2 2