Question (1 Viewer)

[luv2luvurmama]

For inequalities i answer them differently and i dont know if its mathematically corect.For example : Source ; 2003 HSC 4 U, Question 6) c(c) (i) Let x and y be real numbers such that x ≥ 0 and y ≥ 0.Prove that . (x + y)/2 ≥ (xy)^1/2(ii) Suppose that a, b, c are real numbers.Prove that a^4 + b^4 + c^4 ≥ a^2b^2 + a^2c^2 + b^2c^2.(iii) Show that a^2b^2 + a^2c^2 + b^2c^2 ≥ a^2bc + b^2ac + c^2ab.Ok just look at part iii, two and one are easy.What i did to answer it, i used part 2, and used the equation :a^4 + b^4 + c^4 ≥ a^2b^2 + a^2c^2 + b^2c^2. which was proven to be correct.I just let a = (ab)^1/2 b = (bc)^1/2 c = (ac)^1/2 and it substituted it into the equation. It gives the equation required.Can you do this?

 

[Timothy.Siu]

sure why not

 

[untouchablecuz]

For inequalities i answer them differently and i dont know if its mathematically corect.For example : Source ; 2003 HSC 4 U, Question 6) c(c) (i) Let x and y be real numbers such that x ≥ 0 and y ≥ 0.Prove that . (x + y)/2 ≥ (xy)^1/2(ii) Suppose that a, b, c are real numbers.Prove that a^4 + b^4 + c^4 ≥ a^2b^2 + a^2c^2 + b^2c^2.(iii) Show that a^2b^2 + a^2c^2 + b^2c^2 ≥ a^2bc + b^2ac + c^2ab.Ok just look at part iii, two and one are easy.What i did to answer it, i used part 2, and used the equation :a^4 + b^4 + c^4 ≥ a^2b^2 + a^2c^2 + b^2c^2. which was proven to be correct.I just let a = (ab)^1/2 b = (bc)^1/2 c = (ac)^1/2 and it substituted it into the equation. It gives the equation required.Can you do this?

as long as the variables that u are subsitituting satisfy the conditions of the variables that you are substituting into then yes you can; this is almost always the case

 

[luv2luvurmama]

Awesome!!! Thanks!