Test Your Math Skills and Win SBD # 2

monajam (70) in contest • 7 years ago

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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Leave your answer in the comments and explain why did you choose this answer.

All SBD made from this post will be awarded to the participant who chooses the correct answer at the end of the payout period. If there are more than 1 winners, the SBD will be distributed equally among them.

contest math skills sbd win

7 years ago by monajam (70)

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yash0108 (56) · 7 years ago

Excellent post, Amazing. Well done. I'll follow your account to see how you doing. Because i earnings as like you @yash0108

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1 vote

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ahmedhani (49) · 7 years ago

the answer is 1
because if we say that x = -2
-24 = 16 > -22 = 4
power removes negative sign i guess

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1 vote

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kaitochrom (37) · 7 years ago

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1 vote

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faysalmahmud (38) · 7 years ago

ans=2

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1 vote

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universe.laws (52) · 7 years ago (edited)

number 1 , 2 and 3 are true :

False because if x=-1 so 1 < 1 isn't true for x negative
True because x squared will always be positive and x cubed negative thus x^3 < x^2 is true for x negative
True x + 1/x is always negative ex : -1 + 1/-1 = -2 <0 so x + 1/x < 0 is true for x negative
True , if x = -4 thus -4 = 4 or -4 = -4 (because square roots have 2 solutions one negative and one positive) the second solution is true true , and 4. is true for all values of x

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marysent (55) · 7 years ago (edited)

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.

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otage (70) · 7 years ago

Negative x to 3 power is negative. Negative x to 2 power is positive. Therefore No.2 x3 < x2 is true.

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dkmathstats (61) · 7 years ago

For the third one, the restriction is at x = 0.

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marysent (55) · 7 years ago

@dkmathstats, yes but the questions says If X is a negative integer. 0 is a special number.

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dkmathstats (61) · 7 years ago

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 x as a negative, the sum is negative.

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nguyenthanh (63) · 7 years ago

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jmehta (58) · 7 years ago

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xjfinch (25) · 7 years ago (edited)

The answer is 2. Multiplying 2 negatives will give you a positive number. Multiplying a third negative will create a negative number.

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xyzashu (75) · 7 years ago (edited)

2 & 3 must be true.

1 may be true at times but not always e.g. when x = -1
4 is false as square root of a positive number (i.e. square of a negative number) can not be negative because a radical sign is being used.
2 is always true as a square of a negative is positive whereas a cube will always be negative. So it would always be less than a positive no.
3 is always true as sum of two negatives will always be negative. Hence less than zero.

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linhlinhvictoria (55) · 7 years ago

The answer is 2.

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dkmathstats (61) · 7 years ago (edited)

2 & 3 are true.

Q1) False. A counterexample would be x = -0.5 = 1/2. (0.25 > 1/8)

Q2) True. Given that x is negative then

Q3) True. I think there are two ways looking at this. x alone is negative and 1/x would be negative making the sum negative.

The second way would be to find a common denominator. The fraction would be with the top being positive (for all x) and the bottom being negative (as x is negative). This fraction is neagtive.

Q4) False. A counterexample would be x = -1. Left side is -1 and the right side is 1. It would be true if x is negative and the left side was negative x.

Edit: Fixed typos.

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geneeverett (61) · 7 years ago

2 & 3

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monajam (70) · 7 years ago

You didn't explain :)

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satyamsoni (49) · 7 years ago

2
Honestly i don't get what is literally meaning of 3rd option.
But, for choosing one option 2nd option is absolutely correct because square of any negative number is always greater than it's cube.
Cube of negative number is negative hence lesser than it's square.

Waiting for reward 😜😜😜😜

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monajam (70) · 7 years ago

Hahaha.....you are so confident that you would get the reward :P
I like this. :)

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satyamsoni (49) · 7 years ago

Now, i also get the meaning of 3 option it is also true, because summation of two or more than two negative numbers whether it is real or rational number is always lesser than 0.
My my answer is 2&3 .....
Still waiting for reward🤑🤑🤑🤑

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yash0108 (56) · 7 years ago

Thanks ........ I really appreciate it.@yash0108

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science.tech (29) · 7 years ago (edited)

2 , 3 and 4 are True

for x=-1 the equation will be 1<1 this is false
x cubed is always negative (if x negative) while x squared will always be positive so x^3 < x^2 is True
if x= - 1 the equation will be : -2<0 True
if x= - 2 the equation will be : -5/2 <0 True
if x= - 10 the equation will be : -20 <0 True
4.True because the root square will have 2 solutions 1 positive and 1 negative
so if x=-1 the equation will be -1 = -1 True .
If x=-3 the equation will be -3=-3 True

So 1 is false , but 2,3,4 are True

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marcovanhassel (59) · 7 years ago (edited)

Als je nr 3 leest zoals het hoort, is deze ook goed. Er staat namelijk : x + (1/x) < 0 en niet (x + 1) / x . De notitie is onduidelijk en roept dus vraagtekens op. Maar een wiskundige zal beamen dat stelling 2 en 3 beide kloppen. Zie ook het antwoord van @dkmathstats. Stelling 1 klopt trouwens in de meeste gevallen, behalve als x een waarde heeft die tussen -1 en 0 ligt.
Beetje raar raadseltje.....zeker als erbij staat dat er maar één oplossing mogelijk is.

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sbd.giveaway (51) · 7 years ago

Option 2 is true because the square root of negative numbers is always positive.
Option 3 is also true. Suppose x = -1, then -1+1 = 0, and -1<0

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