+0

# Whelp.

+2
127
14
+142

If $$x^2 + \frac{1}{x^2}= 3$$, what is the value of $$\frac{x^2}{(x^2+1)^2}$$?

MY WORKIE:

$$x^2 + \frac{1}{x^2} = 3$$

$$\frac{x^4+1}{x^2}=\frac{3}{1}$$

$$3x^2 = x^4 + 1$$

$$\frac{x^2}{x^4+2x+1}=??????????$$

And that's all I've accomplished...

T-T

Nov 10, 2019
edited by MagicKitten  Nov 10, 2019

#1
+2850
+1

You sure you typed that correctly?

What do you mean by

"If $$x^2+\frac{1}{x^2}$$"

Is it equal to something..?

Nov 10, 2019
#2
+142
0

Sorry I just edited it....

It's equal to 3!

MagicKitten  Nov 10, 2019
#3
+2850
+2

Fixed

Working off of $$3x^2=x^4+1$$

We add 2x2 to both sides

$$3x^2+2x^2=x^4+2x^2+1$$

Factor

$$5x^2=(x^2+1)^2$$

Divide both sides by $$(x^2+1)^2$$

We get:

$$\frac{5x^2}{(x^2+1)^2}=1$$

Divide both sides by 5.

and you get your answer of $$\boxed{\frac{1}{5}}$$

.
Nov 10, 2019
edited by CalculatorUser  Nov 10, 2019
edited by CalculatorUser  Nov 10, 2019
edited by CalculatorUser  Nov 10, 2019
#4
+142
0

????????????????????????????????????????????????

MagicKitten  Nov 10, 2019
#5
+2850
+1

fixed it.

CalculatorUser  Nov 10, 2019
#6
+142
0

Wait- What?

MagicKitten  Nov 10, 2019
#7
+2850
+1

I forgot to add 2x2 to BOTH sides.

don't worry, its fixed. The solution should be correct.

That took me long. Phew.

CalculatorUser  Nov 10, 2019
#8
+142
0

But if you divide by 3, you get 1/3

MagicKitten  Nov 10, 2019
#9
+142
0

oh you just edited it.

gotcha

MagicKitten  Nov 10, 2019
#10
+2850
0

read my solution over again, lol.

CalculatorUser  Nov 10, 2019
#11
+2850
0

me because I attempted 4 different solutions and finally found the right one:

CalculatorUser  Nov 10, 2019
#12
+142
0

WHeLPpPpPPpp

MagicKitten  Nov 10, 2019
#13
+1

I solved it by a different way,

Since x^2+1/x^2=3

as you said, (x^4+1)/x^2=3 also.

Now,

We want to find x^2/(x^2+1)^2

as you factorized it to (Notice you factorized it wrong by not putting power to "2x")

$$x^2/x^4+2x^2+1$$

Well we know that $$x^4+1/x^2=3$$

so solve for x^4+1

$$x^4+1=3x^2$$

Now subsituite this into what we factorized we get:

$$x^2/3x^2+2x^2$$

Simplify,

$$x^2/5x^2$$

simplify more, we get it is equal to 1/5 (As the x's will cancel)

Nov 11, 2019
#14
+142
0

THANK YOU

MagicKitten  Nov 12, 2019