Question

a^2(b^2-c^2)+b^2(c^2-a^2)+c^2(a^2-b^2)​

Answer 1

Step-by-step explanation:

Let

f(x) = a^(2)(b^(2)-c^(2))x^(2)+b^(2)(c^(2)-a^(2))x + c^(2)(a^(2)-b^(2))

<br> We have,

f(1) = a^(2)(b^(2)-c^(2))+b^(2)(c^(2)-a^(2))+c^(2)(a^(2)-b^(2))=0

<br>

therefore" "x = 1

is a root of f(x). <br> Since f(x) is a perfect square. Therefore, its other root is also 1. <br>

therefore" "

Product of the roots = 1. <br>

rArr" "(c^(2)(a^(2)-b^(2)))/(a^(2)(b^(2)-c^(2)))=1

<br>

rArr" "2 c^(2) a^(2) = b^(2) c^(2) + a^(2) b^(2)

<br>

rArr" "(2)/(b^(2))=(1)/(a^(2))+(1)/(c^(2)) rArr a^(2), b^(2), c^(2)

are in H.P