Question

simplify:(5+√5) (5-√5) ​

Answer 1

$(a + b)(a - b) = {a}^{2} - {b}^{2}$

here a = 5

b = √5

so (5+√5) (5-√5) = 5²-√5² = 25 - 5

hence the answer is 20

Answer 2

$\huge \pink {\sf {Given:}}$

$\large \purple {\sf {(5 + \sqrt{5})( 5 - \sqrt{5} )}}$

⠀

$\huge \pink {\sf {To \: Do:}}$

$\large \purple {\sf {Simplify \: The \: Following.}}$

⠀

$\huge \pink {\sf {Identity \: III:}}$

$\large \purple {\sf {(x + y)(x - y) = {x}^{2} - {y}^{2}}}$

⠀

$\huge \pink {\sf {Solution:}}$

$\large \purple {\sf {(5 + \sqrt{5} )(5 - \sqrt{5} )}}$

$\large \purple {\sf {= {(5)}^{2} - {( \sqrt{5} )}^{2}}}$

$\large \purple {\sf {= 25 - 5}}$

$\large \purple {\sf {= 20}}$

⠀

$\huge \pink {\sf {Answer:}}$

$\huge \purple {\sf {20}}$