Test Your Math Skills and Win SBD # 2
If x is negative, which of the following statements must be true?
Note: There may be no or more than one true answers.
- x2 < x4
- x3 < x2
- x + 1/x < 0
- x = √x2
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the answer is 1
because if we say that x = -2
-24 = 16 > -22 = 4
power removes negative sign i guess
4
ans=2
number 1 , 2 and 3 are true :
2 & 4 are true.
No. 1 is false when x = -1.
(-1)^2 =1 & (=1)^4=1, therefore x^2=x^4 when x= -1.
No. 2 is true at all times. A negative number when raised to an odd power will always give you a negative result. A negative number raised by an even power will have a positive result. Therefore, x^3 < x^2 is true.
No. 3 is false since the result of x + 1/x will always be a positive fraction except when x=-1 because it will give you an undefined result. Therefore x + 1/x < 0 is not true.
Example:
-2 +1/-2
= -1/-2
=1/2
1/2 > 0.
No. 4 is true. All positive real numbers has two square roots, one positive square root and one negative square root. The positive square root is sometimes referred to as the principal square root.
Negative x to 3 power is negative. Negative x to 2 power is positive. Therefore No.2 x3 < x2 is true.
For the third one, the restriction is at
x = 0.@dkmathstats, yes but the questions says If X is a negative integer. 0 is a special number.
Zero is neither negative nor positive.
There may be confusion in the third question.
I'm viewing the third question as the first one from the above. Given
xas a negative, the sum is negative.2
2
The answer is 2. Multiplying 2 negatives will give you a positive number. Multiplying a third negative will create a negative number.