Question

if a^2+b^2 vairies as ab then prove that a+b varies as a-b​

Answer 1

Answer:

We have,

a^2 + b^2 varies ab

a^2 + b^2 = k × ab, where k ≠ 0, is a constant.

(a^2 + b^2)/ab = k

(a^2 + b^2)/2ab = k/2

Now, using componendo and dividendo theorem we have,

(a^2 + b^2 + 2ab) / (a^2 + b^2 - 2ab) = (k + 2) / (k - 2)

(a + b)^2 / (a - b)^2 = (k + 2) / (k - 2)

(a + b) / (a - b) =

Since , k is a constant.

So, whatever operation we apply on k, it will be a constant.

(a + b) / (a - b) = constant

(a + b) varies (a - b)

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