Question

please answer this question​

Answer 1

Step-by-step explanation:

one solution will be x=22/3 and y=0, but there are many

Answer 2

Appropriate Question :

Find the values of x and y in

$\sf \leadsto\frac{ \sqrt{7} - 2}{ \sqrt{7} + 2} - \frac{ \sqrt{7} + 2 }{ \sqrt{7} - 2} = x - y \sqrt{7}$

To find :

The values of x and y

Concept :

Rationalisation

To rationalize the denominator means to eliminate any radical expressions in the denominator such as square roots and cube roots. The key idea is to multiply the original fraction by an appropriate value, such that after simplification, the denominator no longer contains radicals.

Solution :

$\sf \leadsto\frac{ \sqrt{7} - 2}{ \sqrt{7} + 2} - \frac{ \sqrt{7} + 2 }{ \sqrt{7} - 2} = x - y \sqrt{7}$

$\sf \leadsto \frac{ (\sqrt{7} - 2)( \sqrt{7} - 2) }{( \sqrt{7} + 2)( \sqrt{7} - 2)} - \frac{ (\sqrt{7} + 2)( \sqrt{7} + 2)}{( \sqrt{7} - 2)( \sqrt{7} + 2)} = x - y \sqrt{7}$

By using identity :

For numerators -

(a - b)(a - b) = (a - b)²

(a + b)(a + b) = (a + b)²

For denominator -

(a + b) (a - b) = a² - b²

$\sf \leadsto \frac{ {( \sqrt{7} - 2)}^{2} }{ {( \sqrt{7}) }^{2} - {(2)}^{2} } - \frac{ {( \sqrt{7} + 2) }^{2} }{ {( \sqrt{7} )}^{2} - {(2)}^{2} } = x - y \sqrt{7}$

As the denominators are same so no need for doing L.C.M

$\sf \leadsto \frac{( \sqrt{7} - 2)^{2} - {( \sqrt{7} + 2) }^{2} }{ {( \sqrt{7} )}^{2} - {(2)}^{2} } = x - y \sqrt{7}$

$\sf \leadsto \frac{ \cancel{ {( \sqrt{7}) }^{2} } - 2 \times \sqrt{7} \times 2 + {(2)}^{2} - \cancel{ {( \sqrt{7} )} + }^{2} - 2 \times \sqrt{7} \times 2 - \cancel{ {(2)}^{2} }}{7 - 4} = x - y \sqrt{7}$

$\sf \leadsto \frac{ - 8 \sqrt{7} }{3} = x - y \sqrt{7}$

Comparing both sides we get

• x = 0

• y = 8/√3