Powers and Roots Practice Test 1

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Question : 17 of 40

Marks: +1, -0

Simplify:

{ 4+√5}/{4-√5}+{ 4-√5}/{ 4+√5}+{√5-1}/{√5+1} .

${ 117- 11√ 5}/ 22$
$117/ 22$
${ 117+11√ 5}/ 22$
${11√ 5}/ 22$
${ 117- 11√ 5}/ 11$

Solution:

{ 4+√5}/{4-√5}+{ 4-√5}/{ 4+√5}+{√5-1}/{√5+1}

={ 4+√5}/{4-√5}×{ 4+√5}/{ 4+√5}+{ 4-√5}/{ 4+√5}×{ 4-√5}/{ 4-√5}+{√5-1}/{√5+1} ×{√5-1}/{√5-1}

=({ 4+√5})^2/{(4)^2-(√5)^2}+({ 4-√5})^2/{(4)^2-(√5)^2}+({√5-1})^2/{(√5)^2-(1)^2}

={21+8√5}/11+{21-8√5}/11+{6-2√5}/4

={84+32√5+84-32√5+66-22√5}/44

={234-22√5}/44

={ 117- 11√ 5}/ 22

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