1. If x+1/y=a+1/b then prove, (x^2) +1/(y^2)= (a^2) +1/(b^2)

[WEIRDBOY]

Need help with these 2 problems [spent hours on them]

1. If x+1/y=a+1/b then prove, (x^2) +1/(y^2)= (a^2) +1/(b^2)

2. If a^2+b^2+c^2=ab+bc+ca then prove a=b=c

 

[Deleted member 4993]

1. If x+1/y=a+1/b Hint: Square both sides

then prove, (x^2) +1/(y^2)= (a^2) +1/(b^2)

2. If a^2+b^2+c^2=ab+bc+ca then prove a=b=c

.

 

[stapel]

Your formatting is unclear. You posted these:

1. If x+1/y=a+1/b then prove, (x^2) +1/(y^2)= (a^2) +1/(b^2)

2. If a^2+b^2+c^2=ab+bc+ca then prove a=b=c

For exercise (1), did you mean any of the following?

. . . . .\(\displaystyle \mbox{i. If }\, x\, +\, \dfrac{1}{y}\, =\, a\, +\, \dfrac{1}{b},\, \mbox{ then prove...}\)

. . . . .\(\displaystyle \mbox{ii. If }\, \dfrac{x\, +\, 1}{y}\, =\, a\, +\, \dfrac{1}{b},\, \mbox{ then prove...}\)

. . . . .\(\displaystyle \mbox{iii. If }\, \dfrac{x\, +\, 1}{y}\, =\, \dfrac{a\, +\, 1}{b},\, \mbox{ then prove...}\)

. . . . .\(\displaystyle \mbox{iv. If }\, x\, +\, \dfrac{1}{y}\, =\, \dfrac{a\, +\, 1}{b},\, \mbox{ then prove...}\)

Same question for the right-hand side of exercise (1).

Need help with these 2 problems [spent hours on them]

When you reply, please include a clear listing of at least one of your efforts on each of these exercises. Thank you!

 

[WEIRDBOY]

If you haven't yet encountered "squaring" (something that is usually covered in pre-algebra), then I'm not sure how you might be expected to work with these rational equations (something that is usually covered in pre-calculus). Have you ever heard of "quadratics" at all?

By the way, your formatting is unclear. You posted these:


For exercise (1), did you mean any of the following?

. . . . .\(\displaystyle \mbox{i. If }\, x\, +\, \dfrac{1}{y}\, =\, a\, +\, \dfrac{1}{b},\, \mbox{ then prove...}\)

. . . . .\(\displaystyle \mbox{ii. If }\, \dfrac{x\, +\, 1}{y}\, =\, a\, +\, \dfrac{1}{b},\, \mbox{ then prove...}\)

. . . . .\(\displaystyle \mbox{iii. If }\, \dfrac{x\, +\, 1}{y}\, =\, \dfrac{a\, +\, 1}{b},\, \mbox{ then prove...}\)

. . . . .\(\displaystyle \mbox{iv. If }\, x\, +\, \dfrac{1}{y}\, =\, \dfrac{a\, +\, 1}{b},\, \mbox{ then prove...}\)

Same question for the right-hand side of exercise (1).


When you reply, please include a clear listing of at least one of your efforts on each of these exercises. Thank you!

I mean this one and the second one I solved it, still stuck with the first one...


\(\displaystyle \mbox{i. If }\, x\, +\, \dfrac{1}{y}\, =\, a\, +\, \dfrac{1}{b},\, \mbox{ then prove...}\)

 

[WEIRDBOY]

To : Stapel

I meant this \(\displaystyle \mbox{i. If }\, x\, +\, \dfrac{1}{y}\, =\, a\, +\, \dfrac{1}{b},\, \mbox{ then prove...}\)

Solved exercise 2

 

[WEIRDBOY]

Hint: Square both sides

I tried and it got me this.....

 

[stapel]

To : Stapel

I meant this \(\displaystyle \mbox{i. If }\, x\, +\, \dfrac{1}{y}\, =\, a\, +\, \dfrac{1}{b},\, \mbox{ then prove...}\)

From the graphic, the exercise is as follows:

. . . . .\(\displaystyle \mbox{1. If }\, x\, +\, \dfrac{1}{y}\, =\, a\, +\, \dfrac{1}{b},\)

. . . . . . . . . .\(\displaystyle \mbox{then prove that }\, x^2\, +\, \dfrac{1}{y^2}\, =\, a^2\, +\, \dfrac{1}{b^2}.\)

You'd previously spent "hours" on this, and now it's been days. What have you tried? Please provide at least one example of your efforts so far, so we can get a feel for what's going on. For instance, you applied the hint you were given in the first response (squaring both sides), and... then what? Thank you!

 

[WEIRDBOY]

From the graphic, the exercise is as follows:

. . . . .\(\displaystyle \mbox{1. If }\, x\, +\, \dfrac{1}{y}\, =\, a\, +\, \dfrac{1}{b},\)

. . . . . . . . . .\(\displaystyle \mbox{then prove that }\, x^2\, +\, \dfrac{1}{y^2}\, =\, a^2\, +\, \dfrac{1}{b^2}.\)

You'd previously spent "hours" on this, and now it's been days. What have you tried? Please provide at least one example of your efforts so far, so we can get a feel for what's going on. For instance, you applied the hint you were given in the first response (squaring both sides), and... then what? Thank you!

Well I got stuck in here (take a look in the attachment), that doesn't look like a '0' to me and I have attached a copy of my frustrated calculation, where I was trying to get the value of ab but failed miserably.

 

[stapel]

Well I got stuck in here (take a look in the attachment), that doesn't look like a '0' to me and I have attached a copy of my frustrated calculation, where I was trying to get the value of ab but failed miserably.

I don't understand what you're doing in the graphic...? It looks like you're starting with what you're supposed to end with, and then are trying to prove... I'm not sure what...?

Try following the hint provided earlier. That is, rather than squaring both sides of the "then", try squaring both sides of the "if".

 

[Ishuda]

Need help with these 2 problems [spent hours on them]

1. If x+1/y=a+1/b then prove, (x^2) +1/(y^2)= (a^2) +1/(b^2)

2. If a^2+b^2+c^2=ab+bc+ca then prove a=b=c

I'm not quite sure what you mean in 1.
x = 100
y = 0.01
a = 199
b = 1

x+1/y = 200 = a +1/b
x² + 1/y² = 20000 \(\displaystyle \ne\) 39602 = a² + 1/b²