Question

solve:
√5 ( 1 + √5 ) x= 2√5 + 4

right answer person will be marked as brainiest.
if answer is with proper explanation​

Answer 1

Answer:

question me error hai

Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

$\sqrt{5} (1 + \sqrt{5} )x = 2 \sqrt{5} + 4$

$= > ( \sqrt{5} + 5)x = 2 \sqrt{5} + 4$

$= > x = \frac{2 \sqrt{5} + 4}{ \sqrt{5} + 5} = \frac{4 + 2 \sqrt{5} }{5 + \sqrt{5} }$

Here,we Rationalising means multiply both numerator and denominator with opposite sign of denominator to remove root from the denominator and shift towards numerator.

$= > x = \frac{4 + 2 \sqrt{5} }{5 + \sqrt{5} } \times \frac{5 - \sqrt{5} }{5 - \sqrt{5} }$

$= > x = \frac{5(4 + 2 \sqrt{5}) - \sqrt{5} (4 + 2 \sqrt{5} )}{ {(5)}^{2} - {( \sqrt{5} )}^{2} }$

Here,in the denominator this identity used :-

$\bold{\boxed{\purple{(x + y)(x - y) = {x}^{2} - {y}^{2} }}}$

$= > \frac{20 + 10 \sqrt{5} - 4 \sqrt{5} - 10}{25 - 5}$

$= > \frac{20 + 6 \sqrt{5} - 10}{20}$

$= > \frac{10 + 6 \sqrt{5} }{20} = \frac{2(5 + 3 \sqrt{5}) }{20}$

$\bold{\boxed{\boxed{\red{ x= \frac{5 + 3 \sqrt{5} }{10} \: or \: x = \frac{1}{2} + \frac{3 \sqrt{5} }{10}}}}}$