Algebra

If x³ + y³ = 9 and x + y = 3, then the value of x⁴+y⁴ is,

x3+y3 = (x + y) × (x2 − xy + y2)

Putting given values of x3+y3 and (x + y)
9 = 3 × ((x+y)2 − 3xy)
  = 3 × (9 − 3xy) 
  = 27 − 9xy

9xy = 18
xy = 2

x4 + y4 = (x2 + y2)2 - 2x2y2
   = (x2 + y2)2 - 2*4 
                                  [Putting value of xy]
   = ((x + y)2 - 2xy)2 - 2*4 
                            [Putting values of (x+y) and xy]
   = (9 - 4)2 - 2*4 
   = 17

If x+1/2x = 2, find the value of 8x³+1/x³

For any real number x the maximum value of 4−6x−x² is at x=,

If 5^√x +12^√x =13^√x then value of x is,

if x = (√2 + 1 )^-1⁄₅ then the value of (x⁵ - ¹⁄_x⁵)

If b² + ¹⁄_b² = 1, then value of b³ + ¹⁄_b³ is ,

E = (b + 1⁄b)(b2 - 1 + 1⁄b2)

If x^1/3 + y^1/3 - z^1/3 = 0 then value of (x + y - z)³ + 27xyz is

x1/3 + y1/3 = z1/3
Now cubing both sides we get 
x + 3x1/3y1/3(x1/3 + y1/3) + y = z
or, (x + y - z) = -3x1/3y1/3z1/3
Cubing again both sides, (x + y - z) = -27xyz.
So answer is zero

then y is equal to,

If ab+bc+ac = 0, then the value of

Following instructions are to be used throughout the quiz:

Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question.
Read both the statements and Give answer
(a) if the data in Statement I alone is sufficient to answer the question, while the data in Statement II alone is not sufficient to answer the question.
(b) if the data in Statement II alone is sufficient to answer the question, while the data in Statement I alone is not sufficient to answer the question.
(c) if the data in each Statement I and Statement II alone is sufficient to answer the question.
(d) if the data even in both Statements I and II together are not sufficient to answer the question.
(e) if the data in both Statements I and II together are necessary to answer the question.

If x,y are integers, then (x² + y²)^1/2 is an integer?
I) x² + y² is an integer
II) x² - 3y² = 0