Inequalities: a > b, (a - b)X^2 > a^2 - b^2, (a - b)X > (a + b)*(a - b); will devidin

[Welson]

Inequalities: a > b, (a - b)X^2 > a^2 - b^2, (a - b)X > (a + b)*(a - b); will devidin

Inequalities
a>b

(a-b)X^2 > a^2 - b^2

(a-b)X > ( a+b ) • (a-b)

deviding by (a-b) will give me less answers to x ?


General question :
X^2 + a^2 = 6 ( x+a ) k -> will deviding by (x+a ) make me lose answes to x since im deviding by a varabile and a parameter ?

 

[Harry_the_cat]

Inequalities
a>b

(a-b)X^2 > a^2 - b^2

(a-b)X > ( a+b ) • (a-b)

deviding by (a-b) will give me less answers to x ?


General question :
X^2 + a^2 = 6 ( x+a ) k -> will deviding by (x+a ) make me lose answes to x since im deviding by a varabile and a parameter ?

I don't really understand your question, but you need to make sure that what you are dividing both sides by is not equal to 0. If it is, then you will "lose" answers.
For example:
Suppose you have the equation: x(x-2)=6(x-2)
If you divide by (x-2) you will get x=6, but you have "lost" the solution x=2 (because in this case x-2=0 and you can't divide by 0)

In the first case you mention, you know that a>b, so therefore a-b > 0 (ie a-b is not 0 therefore it is safe to divide both sides by a-b without "losing" answers AND a-b is positive so the inequality sign stays as is).

 

[stapel]

Inequalities
a>b

(a-b)X^2 > a^2 - b^2

(a-b)X > ( a+b ) • (a-b)

What were the instructions for this above? What are you supposed to be doing with this?

deviding by (a-b) will give me less answers to x ?

I'm sorry, but I don't know what you mean by this...? Since you are given that "a" and "b" are not equal, then dividing through by "a - b" will not create any division-by-zero issues, if that's what you're asking. Since a > b, then a - b > 0, so the inequality sign won't flip around. But since the variable in the inequalities is "X" and we're given no information about how "x" might relate to "X", there is nothing we can say on that regard.

General question :

X^2 + a^2 = 6 ( x+a ) k -> will deviding by (x+a ) make me lose answes to x since im deviding by a varabile and a parameter ?

I'm sorry, but I'm not sure what this means...? Please provide the full and exact text of the original exercise and the complete instructions. Thank you!

 

[Welson]

I don't really understand your question, but you need to make sure that what you are dividing both sides by is not equal to 0. If it is, then you will "lose" answers.
For example:
Suppose you have the equation: x(x-2)=6(x-2)
If you divide by (x-2) you will get x=6, but you have "lost" the solution x=2 (because in this case x-2=0 and you can't divide by 0)

In the first case you mention, you know that a>b, so therefore a-b > 0 (ie a-b is not 0 therefore it is safe to divide both sides by a-b without "losing" answers AND a-b is positive so the inequality sign stays as is).

Unmm all what i wanted to know that when will i lose answers to x and when i wont when there the variable is squared . because i have noticed in the first example that when i devide by a quantaty that doesnt include x as ( a-b ) [ a>b and x > 0 ] i dont lose any answer for x , BUT when i devide a quantaty that includes x like your examble ( dividing by x-2 ) i lose answes as you mentioned , can i say that when we devide by a quantaty that has no x in it ( given that nothing is less than zero so we womt flip signs etc and the variable is squared ) that we wont lose any answers ? But we do lose answers when devide by a quantaty that has x included in it ?

 

[Welson]

I don't really understand your question, but you need to make sure that what you are dividing both sides by is not equal to 0. If it is, then you will "lose" answers.
For example:
Suppose you have the equation: x(x-2)=6(x-2)
If you divide by (x-2) you will get x=6, but you have "lost" the solution x=2 (because in this case x-2=0 and you can't divide by 0)

In the first case you mention, you know that a>b, so therefore a-b > 0 (ie a-b is not 0 therefore it is safe to divide both sides by a-b without "losing" answers AND a-b is positive so the inequality sign stays as is).

Let a=2, b=1, X=1

(a-b)X^2 = 1
a^2 - b^2 = 3

No you cant asume that x must be larger than the sum of a and b -> x >a+b