Question

If x=root 7+root6 and y=root7-root6÷root7+root6 find x+y

Answer 1

GIVEN:

• x = √7 + √6
• y = √7 - √6/√7 + √6

TO FIND:

• x + y = ?

SOLUTION:

y = √7 + √6/√7 - √6

Rationalising the denominator

y = (√7 + √6)(√7 + √6)/(√7 + √6)(√7 - √6)

Using

(a + b)² = a² + 2ab + b²

(a + b)(a - b) = a² - b²

y = (√7)² + 2(√7)(√6) + (√6)²/(√7)² - (√6)²

y = 13 + 2√42/7 - 6

y = 13 + 2√42

Finding x + y

→ √7 + √6 + 13 + 2√42

Hence, x + y = √7 + √6 + 13 + 2√42

Answer 2

${\underline{\huge{\mathbf{\color{pink}{♡ heya \:dost ♡}}}}}$

__________________❤

Given :-

$x = \sqrt{7} + \sqrt{6}$

$y = \sqrt{7 } - \sqrt{6} \div \sqrt{7} + \sqrt{6}$

To find :-

• X + Y

Step by step explanation

• rationalize y

1. $y = \frac{\sqrt{7}-\sqrt{6}}{\sqrt{7}+\sqrt{6}}$

multiplying numerator and denominator by same no.

$y = \frac{\sqrt{7}-\sqrt{6}}{\sqrt{7}+\sqrt{6}} * \frac{\sqrt{7}-\sqrt{6}}{\sqrt{7}-\sqrt{6}}$

$y = \frac {(\sqrt7-\sqrt6)^2}{\sqrt7^2 - \sqrt6^2}$

$y = \frac{7 + 6 - 2 * \sqrt 7 * \sqrt6}{1}$

$y = 13 - 2\sqrt{42}$

• putting values

x + y = $\sqrt 7 + \sqrt 6 + 13 - 2\sqrt{42}$

Answer :-

$\sqrt 7 + \sqrt 6 + 13 - 2\sqrt{42}$

_________________❤

${\underline{\huge{\mathbf{\color{pink}{♡ thank\:you ♡}}}}}$