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Basic of Logarithms
medium
જો $x = \sqrt 7 + \sqrt 3 $ અને $xy = 4,$ તો ${x^4} + {y^4}=$
A
$400$
B
$368$
C
$352$
D
$200$
Solution
(b) $x = \sqrt 7 + \sqrt 3 ,\,\,xy = 4$
$ \Rightarrow $$y = {4 \over x} = {4 \over {\sqrt 7 + \sqrt 3 }} = {{4(\sqrt 7 – \sqrt 3 )} \over {7 – 3}} = \sqrt 7 – \sqrt 3 $
${x^4} + {y^4} = {({x^2} + {y^2})^2} – 2{x^2}{y^2}$
$ = {[{(x + y)^2} – 2xy]^2} – 2{(xy)^2} = {[{(2\sqrt 7 )^2} – 8]^2} – 2\,.\,{4^2} = 368$.
Standard 11
Mathematics
