Question

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

Answer 1

Answer:

2a square and 2b square

Step-by-step explanation:

2a^2+2b^2+2ab+2a^2+2b^2-2ab

Answer 2

Answer:

if a² +b² varies a²-b², prove that a varies b​. (proved)

Step-by-step explanation:

Given, a² +b² varies a²-b².

Hence, (a² +b²)  = k (a²-b²)                           [k is a variation constant]

$or, k=\frac{a^2+b^2}{a^2-b^2} \\or, \frac{k+1}{k-1} = \frac{(a^2+b^2)+(a^2-b^2)}{(a^2+b^2)-(a^2-b^2)}\\or, \frac{k+1}{k-1} = \frac{a^2+b^2+a^2-b^2}{a^2+b^2-a^2+b^2}\\or, \frac{k+1}{k-1} = \frac{2a^2}{2b^2}\\or, \frac{k+1}{k-1} = \frac{a^2}{b^2}\\or, \frac{\sqrt{k+1}}{\sqrt{k-1}}= \frac{a}{b}\\or, a = (\frac{\sqrt{k+1}}{\sqrt{k-1}}) b$

As k is a constant, $\frac{\sqrt{k+1}}{\sqrt{k-1}}$ is a constant. Hence, a varies b​.