Question

$\huge\underline\mathtt{Solve it guys}$


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Answer 1

$\huge\underline\mathtt\color{crimson}{♡Be brainly♡}$

Answer 2

$\huge\underline\mathtt{Solution: }$

Question

If $x \infty y$ ,let us prove that x+y $\infty$ x-y.

Answer:

$x \infty y$

$\implies x = ky[Where \: K \: is \: non-zero\: constant] \\ \implies \frac{x}{y} = \frac{k}{1} \\ \implies \frac{x + y}{x - y} = \frac{k + 1}{k - 1}[Componendo\: and\: Dividendo]$

$\implies x + y = \frac{k + 1}{k - 1} (x - y) \\Since,\: x + y \infty x - y$

(Here,$\frac{k + 1}{k - 1} \:is \: non-zero \: constant$

(Proved)

$\rule{300}{2}$

Question:

If $x \infty y \: and \: u \infty z$,let us prove that $xu \infty yz$ and $\frac{x}{u} \infty \frac{y}{z}$

Answer:

Prove 1

$x \infty y$ , $u \infty z$

$\implies x= k y$----------(1)

And,

$\implies u= l z$---------(2)

Now,by multiplying both the equations, we get,

$\implies xu = ky.lz \\ \implies xu = kl.yz \\ xu \infty yz$

(Here,kl =non-zero constant

(Proved)

Prove 2

$x \infty y$ , $u \infty z$

$\implies x= k y$----------(1)

And,

$\implies u= l z$---------(2)

Now,by dividing both the equations, we get,

$\implies \frac{x}{u} = \frac{ky}{lz} \\ \implies \frac{x}{u} = \frac{k}{l} . \frac{y}{z} \\ \implies = \frac{x}{u} \infty \frac{y}{z}$

(Here,$\frac{k}{l}$ is non-zero constant)

(Proved)

$\rule{300}{2}$

$\huge\underline\mathtt{ThankUhh}$