aditc aditc
  • 25-08-2019
  • Mathematics
contestada

Is the following true for all positive values of a and b: If a^2>b^2, then a>b

Respuesta :

Codeman90 Codeman90
  • 25-08-2019

Answer:

Yes, that is correct.

Step-by-step explanation:

a would always have to be greater than b since you're just multiplying each variable by itself.

Answer Link
freckledspots freckledspots
  • 25-08-2019

Answer:

Yes

Step-by-step explanation:

[tex]a^2>b^2[/tex] means [tex]a^2-b^2>0[/tex].

Factoring the left hand side gives me:

[tex](a-b)(a+b)>0[/tex]

Since [tex]a,b[/tex] are positive then [tex]a+b[/tex] is positive so dividing both sides by this will not effect the direction of the inequality:

[tex]a-b>0[/tex]

Adding [tex]b[/tex] on both sides gives:

[tex]a>b[/tex]

Answer Link

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