Question

if a²+ b² varies ab, let us prove that a+b varies a-b​

Answer 1

Step-by-step explanation:

First let's take

(a+b)²x(a-b)²

=(a+b)(a+b)x(a-b)(a-b)

=(a+b)(a-b)x(a+b)(a-b)

=(a²-b²)x(a²-b²)

=(a²-b²)²

That's it

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Answer 2

${\huge {\mathfrak {Answer :-}}}$

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We have,

a^2 + b^2 varies ab

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

$\implies$ (a^2 + b^2)/ab = k

$\implies$ (a^2 + b^2)/2ab = k/2

Now, using componendo and dividendo theorem we have,

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

$\implies$ (a + b)^2 / (a - b)^2 = (k + 2) / (k - 2)

$\implies$ (a + b) / (a - b) = $\sqrt { (k + 2) / (k - 2) }$

Since , k is a constant.

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

$\implies$ (a + b) / (a - b) = constant

$\implies$ (a + b) varies (a - b)

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