Question

Find the value of X and y if 7+4√3_7-4√3 = X + y √3​

Answer 1

Step-by-step explanation:

$(7 + 4 \sqrt{3} )(7 - 4 \sqrt{3} ) = x + y \sqrt{3}$

using identity

$(x + y)(x - y) = {x}^{2} - {y}^{2}$

$( {7)}^{2} - ({4 \sqrt{3} )}^{2} = x + y \sqrt{3}$

$49 - 16 \times 3 = x + y \sqrt{3}$

$49 - 48 = x + y \sqrt{3}$

$1 = x + y \sqrt{3}$

$x + y = \frac{1}{ \sqrt{3} }$

$x + y = \frac{1}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt[]{3} }$

$x + y = \frac{ \sqrt{3} }{3}$

Multiple by 3 both sides...

$3x + 3y = \sqrt{3}$