Given two numbers x and y such that
1. x3 + y3 = 9
2. x + y = 3
Find the value of x4+y4
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
The value of x+1/2x is given as 2, then find the value of 8x3+1/x3
x3 + 1/8x3 + 3.x.1/2x(x + 1/2x) = (x+1/2x)3
x3 + 1/8x3 + 3 = 23
x3 + 1/8x3 = 5
8x3 + 1/x3 = 5.8 = 40
If x takes only real numbers. For what value of x, the value of the expression: 4−6x−x2 will be maximum?
Differentiate and equate to 0 6+2x =0 x=−3
For what value of x, the following equation: 5√x +12√x =13√x will be true?
None of the above
for, x=2 and 3 also not possible
If value of x = (√2 + 1 )-1⁄5 then the find the value of (x5 - 1⁄x5)
If the value of b2 + 1⁄b2 = 1, then find the value of b3 + 1⁄b3
None of the above
E = (b + 1⁄b)(b2 - 1 + 1⁄b2)
(ab + bc + ca)/[(a+b+c)(abc)]
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