Question

question no.13 plzz fast........​

Answer 1

Given :

$\tt{ {\dfrac{ {\sqrt{7}} + {\sqrt{5}} }{ {\sqrt{7}} - {\sqrt{5}} }} - {\dfrac{ {\sqrt{7}} - {\sqrt{5}} }{ {\sqrt{7}} + {\sqrt{5}} }} }$



Solution :

$\tt{\Rightarrow {\dfrac{ {\sqrt{7}} + {\sqrt{5}} }{ {\sqrt{7}} - {\sqrt{5}} }} × {\dfrac{ {\sqrt{7}} + {\sqrt{5}} }{ {\sqrt{7}} + {\sqrt{5}} }} - {\dfrac{ {\sqrt{7}} - {\sqrt{5}} }{ {\sqrt{7}} + {\sqrt{5}} }} × {\dfrac{ {\sqrt{7}} - {\sqrt{5}} }{ {\sqrt{7}} - {\sqrt{5}} }} }$



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



$\tt{\Rightarrow {\dfrac{ ( {\sqrt{7}} + {\sqrt{5}} )^2 }{ ( {\sqrt{7}} )^2 - ( {\sqrt{5}} )^2 }} - {\dfrac{ ( {\sqrt{7}} - {\sqrt{5}} )^2 }{ ( {\sqrt{7}} )^2 - ( {\sqrt{5}} )^2 }} }$



${\boxed{\tt{(a + b)^2 = a^2 + 2ab + b^2}}}$

${\boxed{\tt{(a - b)^2 = a^2 - 2ab + b^2}}}$



$\tt{\Rightarrow {\dfrac{ ( {\sqrt{7}} )^2 + ( {\sqrt{5}} )^2 + (2)( {\sqrt{7}} )( {\sqrt{5}} ) }{ 7 - 5}} - {\dfrac{ ( {\sqrt{7}} )^2 + ( {\sqrt{5}} )^2 - (2)( {\sqrt{7}} )( {\sqrt{5}} ) }{ 7 - 5}} }$



$\tt{\Rightarrow {\dfrac{7 + 5 + 2 {\sqrt{35}} }{2}} - {\dfrac{7 + 5 - 2 {\sqrt{35}} }{2}} }$



$\tt{\Rightarrow {\dfrac{7 + 5 + 2 {\sqrt{35}} - (7 + 5 - 2 {\sqrt{35}} )}{ 2}} }$



$\tt{\Rightarrow {\dfrac{4 {\sqrt{35}} }{2}} }$



$\tt{\Rightarrow 2 {\sqrt{35}} }$



On comparing with a + b√35, we get



a + b√35 = 0 + 2√35




Hence, $<b><I><u>a = 0 and b = 2</b></u></I>$