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16 Nov 2021, 09:45
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Difficulty:
45%
(medium)
Question Stats:
69% (02:18) correct
31%
(02:40)
wrong
based on 347
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The expression \((\frac{1}{\sqrt{8 - \sqrt{63}}} +\frac{1}{\sqrt{8 +\sqrt{63}}})^2 =\)
(A) 21
(B) 20
(C) 19
(D) 18
(E) 17
(A) 21
(B) 20
(C) 19
(D) 18
(E) 17
16 Nov 2021, 10:08
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Bunuel
Multiply by their conjugates to remove denominator.
\((\frac{1}{\sqrt{8 - \sqrt{63}}} +\frac{1}{\sqrt{8 +\sqrt{63}}})^2 =\)
\((\frac{ \sqrt{8 + \sqrt{63}}}{\sqrt{8 - \sqrt{63}}* \sqrt{8 + \sqrt{63}}} +\frac{ \sqrt{8 - \sqrt{63}}}{\sqrt{8 +\sqrt{63}}* \sqrt{8 - \sqrt{63}}})^2 =\)
\((\frac{ \sqrt{8 + \sqrt{63}}}{\sqrt{64 - {63}}} +\frac{ \sqrt{8 - \sqrt{63}}}{\sqrt{64 -{63}}})^2 =\)
\( (\sqrt{8 + \sqrt{63}}+\sqrt{8 - \sqrt{63}})^2\)
\( (\sqrt{8 + \sqrt{63}})^2+(\sqrt{8 - \sqrt{63}})^2\) \( +2(\sqrt{8 + \sqrt{63}}*\sqrt{8 - \sqrt{63}})\)
\(8+\sqrt{63}+8-\sqrt{63}+2=18\)
OR
\((\frac{1}{\sqrt{8 - \sqrt{63}}} +\frac{1}{\sqrt{8 +\sqrt{63}}})^2 =\)
\((\frac{ \sqrt{8 +\sqrt{63}}+ \sqrt{8 - \sqrt{63}}}{\sqrt{8 - \sqrt{63}}*\sqrt{8 +\sqrt{63}}})^2 =\)
\( (\sqrt{8 + \sqrt{63}}+\sqrt{8 - \sqrt{63}})^2\)
\( (\sqrt{8 + \sqrt{63}})^2+(\sqrt{8 - \sqrt{63}})^2\) \(+2 (\sqrt{8 + \sqrt{63}}*\sqrt{8 - \sqrt{63}})\)
\(8+\sqrt{63}+8-\sqrt{63}+2=18\)
Hi chetan2u, thank you for sharing your approach! I tried solving using identities as a first approach.
I then tried solving with your approach (multiplying by conjugate) and I am still getting it wrong. Can´t see where I commited the error
Any input would help inmensly!
Best regards
I then tried solving with your approach (multiplying by conjugate) and I am still getting it wrong. Can´t see where I commited the error
Any input would help inmensly!
Best regards
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