All Questions

A number written in base a is 123_a. The same number written in base b is 146_b. What is the minimum value of a + b?

What is B ?

Find x :

\(x\left\{{}\begin{matrix}x+x\\x-x\\x\times x\end{matrix}\right.\)

If a is the even number, the total of a + a is the even number or the odd number?

Give that the rectangle ABCD as shown. Prove that : the perinmeter of the rectangle ABCD is equal the area of the rectangle ABCD.

28) Given x² + 5y² - 4xy - x + 2y - 6 = 0

Find the max and min values of A = x - 2y

27) Given x, y, z \(\in Z\) and

a = x² - yz                             c = z² - xy 

b = y² - xz

Prove that: a³ + b³ + c³ - 3abc is a square number.

26) Find x, y, z such that:

\(\left\{{}\begin{matrix}x+y+xy=8\\y+z+yz=15\\z+x+zx=35\end{matrix}\right.\)

Three containers A, B, and C contain a total of 48 apples. First, 6 apples are taken from A and are put into B. Second, 9 apples are taken from B and are put into C. Now, each container has the same number of apples. What is the original number of apples in container A? 

Ali has 5 consecutive numbers while Ben has 7 consecutive numbers, none of the Ali’s number is in the group of Ben’s numbers. If the second number of Ali’s number is 5 and the sum of Ali’s and Ben’s numbers are 128. What is the largest number of Ben’s number?