(x+Y) : (x-y)=4:1 so (x2+y2) : (x2-y2)=?

Question

(x+Y) : (x-y)=4:1  so (x2+y2) : (x2-y2)=?

mathslover · Answer

are there any options given ?

mathslover · Answer

attachment

mathslover · Answer

we can solve this further easily but before that i want to know that whether are the options given ? so that i can know that in which terms u want answer

anonymous · Answer

You are going very difficult @mathslover ..

mathslover · Answer

:) that is my way sorry .... 
let me think of an easy one @waterineyes  wait

anonymous · Answer

Well, what is the profit of your way if the asker does not understand it..

mathslover · Answer

sorry have to go now..will answer soon @waterineyes  please help him .. @waterineyes i am thinking about this can u wait or just answer

anonymous · Answer

Ya, I can help you must leave now..

mathslover · Answer

i am getting $\sqrt{236}xy/15$

anonymous · Answer

See, we have given;

(x + y)/(x - y) = 4/1

So, Cross multiplying we get,

4x - 4y = x + y

3x = 5y

Or x = 5y/3

Put this in the required expression:

$$(x^2 + y^2)/(x^2 - y^2) = (25y^2/9 + y^2)/(25y^2/9 - y^2) = y^2(25/9 + 1)/y^2(25/9 - 1)$$

$$= (25/9 + 1)/(25/9 - 1) = 34/16 = 17/8$$

$$(x^2 + y^2)/(x^2 - y^2) = 17/8 = 17:8$$

mathslover · Answer

great work @waterineyes

anonymous · Answer

it can be easily done by using componendo and dividendo property of ratios and proportions.....

anonymous · Answer

I don't know much about that so I had to go with this method...

anonymous · Answer

I think it is like:

(x + y + x - y)/(x + y - x + y) = (4+1)/(4 - 1)

2x/2y = 5/3

x/y = 5/3

Or Squaring both the sides,

$$x^2/y^2 = 25/9$$

Using again Componendo And Dividendo,

$$(x^2 + y^2)/(x^2 - y^2) = (25 + 9)/(25 - 9) = 34/16 = 17/8$$

Yes guys, this is very simple method to solve these type of questions...