Inequality help? (1 Viewer)

[atamiabwv]

I'm having trouble answering these questions, especially b) and c). Any help/answers would be greatly appreciated

View attachment maths.bmp

View attachment a and b.bmp

 

[fan96]

b) R.T.P.

Squaring both sides,





Multiplying both sides by 16,





Can you finish it from here?

c) seems to be missing some context... what are and ?

Also this looks like it would belong in the Mathematics subforum (i.e. the 2U one).

 

[sida1049]

For part (b), literally follow the hint: after squaring both sides and simplifying, you should get
32 + 16√2 < 38 + 12√2,
which simplifies further to
√2 < 3/2,
which is the same inequality in part (a).

I can't help you with part (c), since I don't know what a and b are.

 

[atamiabwv]

b) R.T.P.

Squaring both sides,





Multiplying both sides by 16,





Can you finish it from here?

c) seems to be missing some context... what are and ?

Also this looks like it would belong in the Mathematics subforum (i.e. the 2U one).

Yes sorry this is in the wrong forum! But I'm a bit confused at how 6+√2/4 squared does not give 36+2/16? I've attached a picture above now showing the values for a and b. Sorry, I probably seem like a maths noob

 

[atamiabwv]

For part (b), literally follow the hint: after squaring both sides and simplifying, you should get
32 + 16√2 < 38 + 12√2,
which simplifies further to
√2 < 3/2,
which is the same inequality in part (a).

I can't help you with part (c), since I don't know what a and b are.

Thanks for your help!! I've now attached values for a and b

 

[fan96]

how 6+√2/4 squared does not give 36+2/16?

With , :

 

[atamiabwv]

With , :

That makes more sense now, thank you heaps

 

[atamiabwv]

b) R.T.P.

Squaring both sides,





Multiplying both sides by 16,





Can you finish it from here?

c) seems to be missing some context... what are and ?

Also this looks like it would belong in the Mathematics subforum (i.e. the 2U one).

Do you perhaps have any idea how to do part (c) now, after the attachment?

 

[fan96]

Do you perhaps have any idea how to do part (c) now, after the attachment?

Given

R.T.P.

Square both sides





Divide both sides by 64:





This is starting to look like the result of part b). Can you take it from here?

 

[atamiabwv]

Given

R.T.P.

Square both sides





Divide both sides by 64:





This is starting to look like the result of part b). Can you take it from here?

That's really helpful, thank you very much! I've taken it a bit further for the LHS, but I'm not sure what do to for the RHS. I've attached my working: View attachment IMG_6433.bmp

 

[fan96]

That's really helpful, thank you very much! I've taken it a bit further for the LHS, but I'm not sure what do to for the RHS. I've attached my working: View attachment 34519

Don't square it - you want to get it to the result in part b).

You'll be able to see the answer by doing just one subtraction.

 

[atamiabwv]

Don't square it - you want to get it to the result in part b).

You'll be able to see the answer by doing just one subtraction.

Hmm I’ve tried subtracting -2 from both sides, other than that I don’t know what else I could really subtract. I’m still not getting the answer, and my classmates are confused too. Sorry for all the hassle

 

[fan96]

Subtract 2:





Multiply by -1 (which flips the inequality sign)





Which is the result in b)