If m : n = 5 : 4 then what is the value of $$\left(m^2 + n^2\right) : \left(m^2 - n^2\right)$$?
If m : n = 5 : 4.
Let's assume m = 5y and n = 4y.
Value of $$\left(m^2 + n^2\right) : \left(m^2 - n^2\right)$$ =Â $$\left(\left(5y\right)^2+\left(4y\right)^2\right):\left(\left(5y\right)^2-\left(4y\right)^2\right)$$
= $$\left(25y^2+16y^2\right):\left(25y^2-16y^2\right)$$
=Â $$41y^2\ :\ 9y^2$$
= 41 : 9
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