Question

if x√243=y√867,where x and y are co prime numbers,then the value of (x-y) is​

Answer 1

The value of (x - y) is "8".

Step-by-step explanation:

We have,

x × $\sqrt{243}$ = y × $\sqrt{867}$

⇒ x × $\sqrt{81 \times\ 3}$ = y × $\sqrt{3 \times\ 17 \times\ 17}$

⇒ 9x × $\sqrt{ 3}$ = 17y × $\sqrt{3}$

⇒ 9x = 17y

⇒ $\frac{x}{y}$ = $\frac{17}{9}$

∴ x = 17 and y = 9 [∵ x and y are co-prime numbers]

∴ x - y = 17 -  9 = 8

Hence, the value of (x - y) is "8".

Answer 2

Given: $x\sqrt{243}=y\sqrt{867}$ where $x$ and $y$ are co-prime numbers.

To Find: What is the value of $(x-y)$.

Step-by-step explanation:

In question given is,

  $x\sqrt{243}=y\sqrt{867}$

Factor of $243$ is $3,3,3,3\ and\ 3$

And factor of $867$ is $3,17\ and\ 17$

So,

⇒$x\sqrt{3\times 3\times 3\times 3\times 3}=y\sqrt{3\times 17\times 17}$

⇒$9x\sqrt{3}=17y\sqrt{3}$

Cancel $\sqrt{3}$ on both sides,

⇒$9x=17y$

⇒$\frac{x}{y}=\frac{17}{9}$

∴ $x=17\ and\ y=9$ [∵ $x$ and $y$ are co-prime numbers]

∴ $(x-y)=17-9=8$

Therefore, The value of $(x-y)$ is $8$.